I'm not sure if we need an eval. And I don't know what good that would do if we did. Nor would I know how to go about getting one.
You start with your pediatrician. Are you in the US? The pediatrician will have screening tools for ADHD, developmental delays, etc.
People are giving you lots of ideas, but they're details. Sure it might be a strategy to reduce tech or use headphones or this or that, but you don't know WHY yet. You haven't really determined what's going on. So you go to the pediatrician, talk with him, let him refer you. Don't let him diagnose, because this dc is actually old enough for a full psych eval and complete information. Like if he just says oh it's ADHD and gives you a scrip for meds, what good did that do? Meds can help, but it didn't get you a screening for motor planning problems, didn't get you information on his working memory or executive function, didn't get you screenings on language issues, SLDs, etc.
The research shows that people who start with behavioral methods *before* meds for ADHD actually have more satisfactory outcomes than people who start with meds and bring them in later. Again, that's something the ped can refer you for. Or the psych can refer you after the eval.
I can tell you there are kids with ADHD at 7/8 who do *not* have the issues with emotional regulation, compliance, sense of group plan, noticing what is appropriate behavior in a setting, etc. that your ds is having. I'm looking at that, as someone whose boy has pretty challenging behaviors and going wow, I'd really want to make sure I knew what was going on. Usually people on the boards aren't telling EVERYTHING. I'm looking at some of what you've written (refusals to work, getting up and walking around during meals, etc.) and going ok my ds does/did that and I know *why* he did that. I would be concerned.
What would change? If you go to SocialThinking.com and start reading, you'll find that many kids have social thinking deficits underlying their behaviors. The social thinking deficits can span labels, so you can have them if the issue is ADHD or ASD or NVLD or Tourettes or... So we don't have to die on a hill of what the diagnosis is. A diagnosis opens doors and gets you insurance coverage. The big thing is to see the Social Thinking deficits and go ok *why* does he not understand the group plan here, why is he not able to use age-appropriate strategies and regulate his emotions, why is he not able to perspective take and see that his non-compliance is hurting your feelings, why does he not catch on to cause/effect that his non-compliance is keeping him from doing activities he'd really like to do, why is he not self-advocating (expressing his emotions appropriately), etc., kwim?
So that's why you would get behavioral help, because there are curricula they can work through with him to help his social thinking, to help him start noticing how his behaviors affect others, to help him start regulating his emotions and making better choices rather than being a victim of his body.
Right now, he's a victim of his body and his development. Whatever his body says do, he largely does. He's doing better in high structure environments, and that's a really good sign! Personally, I think you're fighting a losing battle. He's likely to need meds, OT, social thinking instruction, and a very high structure environment to succeed. For you to provide that while taking care of a toddler is almost impossible. My dd has very significant ADHD and my kids were 10 years apart. That age/stage was VERY hard, and it was basically a losing battle. Having done what you've done, I'm saying it's a losing battle.
My dd was old enough to work independently, so we tried to make it work. There were pros and cons to that. Because of the closeness of your kids' ages, personally I would enroll him in school. He seems to respond well to structure, and school is extremely structured. It would give him predictability, routine, clear expectations, consequences. The school will have a process for behavioral supports (positive behavioral supports!) and can do a 504 or IEP to bring in supports to help him succeed. The school may have people on staff trained in Social Thinking, or you could do that curriculum with him after school.
If you wish to continue to homeschool him, you'll want a full psych eval, any other evals they refer him for (OT, etc.), social thinking instruction, and probably meds. I would then seriously consider enrolling your toddler in a preschool or bringing in a mother's helper. It's not acceptable to plunk a toddler in front of large amounts of tech. The toddler needs language instruction and interaction.
If you want to change what is happening (complete non-compliance on school work), you'll have to change something. Merely being home does NOT make magic happen. Some things are very, very hard. If you want to change something today? Start using alarms and get some structure and routine to your lives. Start small, with just one alarm. Is there something you *usually* do but sometimes forget? Like eating breakfast? I do that. With my ds, that's where we started. ADHD responds well to structure, clear expectations, a plan.
As far as school, I would only attempt 15 minutes, not 2 hours or whatever, and I would require it. I would tell him we're going to set the alarm for such and such time (10:00 am), and when it goes off we're going to do 15 minutes of math games. And before that time, at 9:30, 9:45, etc. I would remind him of the upcoming plan. And at 9:50 I would transition your toddler to her activity that she'll do from 9:50-10:15. I would set up a reward (that he can lose) as motivator, so he is looking forward to something that follows when he complies. Since our weather is awesome, that thing would be the park! So I would tell him ahead of time, while you're explaining the plan, that at 10:15, when you finish math, you'll go to the park. Tell him clearly your expectations for behavior and follow through with the reward. Make sure your expectations are within reach so he's likely to succeed.
Do that every day for a week. Now you have 15 minutes of math going. Then you start setting an alarm for another thing. I would say breakfast or weekly room cleaning or maybe another thing that is schoolish that he might prefer, like read alouds. So you're ramping up, adding one thing at a time, building in motivators, alternating preferred and non-preferred.
My ds is extremely challenging to work with. These are strategies we use with him. Alarms, clear expectations, plan on the calendar, motivators. We use Zones of Regulation, which you can see on the Social Thinking site. My ds has a private office, a bedroom that we converted. He really needs his own space. Otherwise he'll just wander and be POOF, gone! Now we're working on working other places. We can do that a little! It's a goal with our team to GET him to where he can self-regulate and work other places and be calm and on-task. But I'm just saying don't make that a hill to die on. Some kids really need a distraction-free environment where they know when they're in that space this is what they do. Then, after a while, their brain says oh THAT'S what she wanted, and they can slowly start to do it other places. But for now, you might want to set him up an office. When you're in that office working for that 15 minutes, you make it very high value, with motivators and positive experiences, and NO TODDLER. Don't bring that toddler in there. Hire a mother's helper, plunk in front of leap frog, put in an adjacent room for some quiet play with a timer and a gate, whatever. You go in the private office with your ds, using the alarm, using the timer, knowing the plan, and you SHUT THE DOOR.
Do not put anything to distract him in the room. No bed, dressers, interesting artwork, things to play with, things to worry about. When we made our space, I wanted fish and this and that. The behaviorist was like nope, nope, need it calm, don't want his brain WORRYING about all those other things and monitoring them. We want him monitoring HIMSELF, not those other things. It's all he can handle, just to self-monitor.
Don't know if I've posted pics of my ds' office. I don't see them on Flickr, must not have. Well maybe I'll take some. I'm hoping to rearrange some time this week. He's been in his arrangement a year, and we're going to change how we're doing things. When we started, his space needs were very much like K5/1st, with small nooks. Now I think we're going to go to work stations and sort of a different arrangement, maybe trade out some furniture. So it's totally going to change!
We use whiteboards so he can see the plan. Any worker who works with him writes the plan on the whiteboard, so they can check it off as he goes. It's not like he doesn't get to contribute to the plan. He could MAKE the plan, for all we care! It's not about unschooling vs. this or that. It's about having a plan, having structure, knowing the plan, being on the plan, saying when you need a break, that kind of thing.
Would your ds go into 2nd or 3rd in a school? It's something to consider. My ds has an IEP, and I just had an intervention specialist in to talk through things. I can tell you in 3rd the structure really changes. Actually they make that transition in 2nd. Your ds would need supports to go into a structured environment like that and have expected behavior. Most kids, even kids with ADHD, have no issues going from homeschool to an environment like that. It's not you or something you've done. It's HIM. Some kids are just entropy in action. He's going to need a lot of structure and support to succeed. These discussions of tech, etc. are nice, but it kind of implies that if you just pulled that ONE THING, wow everything would get all better. That's not why he's where he's at. He's got some internal dysregulation, and he's going to need some supports. Being careful about tech will be part of it. We use tech as a motivator! No compliance, you lose. Don't obey, you lose. You don't obey me, I take the kindle. You have to EARN IT BACK. So tech can be a motivator!
You're the adult and you have to control what happens. Not with meanness but with finding out what is going on and how much structure he needs to succeed and by assembling a team approach that can make that amount of structure happen. It's not about WHO does it, only that it gets done.