My oldest is currently in PS, so that colors my perspective, but as the Mom of a kid with a chronic illness who was a sick infant, I have to say that I was grateful to have school and at that time it was mostly preK and day care available for my other kids. Caring for my sick baby was an absolutely around the clock and sometimes life or death matter that it left very little of me available physically, emotionally, for the other kids. Having care for the other kids during the day allowed me to focus on the sick child and then during the hours the others were home I made that extra effort to be there for them and returned to sick care after bedtime.
Even now, when he isn't acutely ill, we might have 8-12 medical appointments in a busier month, not counting those last minute sick kid visits, and each one can easily take 2-3 hours just in the office. Specialists here often only see patients with a specific condition 1 day per week and sometimes as little as 2 half-days per month meaning appointments are hard to get and there is really no flexibility on their end.
I do take all the kids during school breaks or if its my oldest who needs to see a specialist and I think the hardest part is needing but not being able to focus on my conversation with the Drs. My 2 and 4 year olds are climbers/jumpers and after 2-3 hours in a small room they are usually no longer on their best behavior. Keeping an eye on them so I can discuss symptoms, treatment, test results, etc. is just a million times harder with everyone in the room. So, if there is any other option, I would consider it. We don't have other family and friends are great but can only do so much. If you aren't opposed to a short-term use of school, then it might be a good temporary solution for your family.