Hi,
So sorry to hear of the hurdles thrown at your family. Even if dementia is not part of your mother's diagnosis, please take time to read The 36-hour Day. It is a family guide to caregiving and will have resources for you as you become the primary caregiver. It has chapters on taking care of yourself and children too. Also, check with the Social Worker at her current facility to try to get as much help at home as possible. There are many aging in place and caregiver support groups where you may be able to get volunteers to give you some help or free time by sitting and keeping your mother company (and safe) while you run errands or take a breather. You may have to convince your mother's partner to do more--explain that this is what is done for someone you love. Also, if you do have other family that can help, try to get a commitment of help (bring dinner every Tuesday, give you a Saturday afternoon away, take Mom for a drive, etc.).
For school, if you follow the basics in the Well-Trained Mind, I think it can be done inexpensively with lots of library resources. Just focus on the basics with lots of outside reading until your life settles down. At my library, I can order books online and they notify me when they are ready to pick up. I hope yours offers a similar service. I go through the Well-trained mind or other lists (from here) for history, literature, and science and order books. If they do not have it, I move on to the next on the list. The librarians also could be a great reference for suggesting books. Audio books are great too for listening during car rides to medical appointments or arts and crafts.
If you do not have a copy of the Well-Trained mind, contact me. I have two and could part with one. The older version doesn't have Susan Wise Bauer's writing course, but we have found that course to be pretty independent for daily work, especially for Writing with Skill. At 5th grade, your daughter may do better with Writing with Ease if she hasn't used the course before. That is more teacher involved, but still not so much if you are using other independent sources. SWB recommends Writing with skill for 6th and above. My kids are older so I have already parted with many of the younger grade books or I would share. In 5th grade, my kids used the history and science encyclopedias as spines and did the extra reading/projects/experiments as we could.
For typing: BBC Dance mat typing was easy/independent and best of all--free. https://www.dancemattypingguide.com/dance-mat-typing-level-1/. Both my kids are self taught using this program.
It sounds like you have other good recommendations for math and science. For a 5th grader, try to balance computer work with books and paper. I hope she'll be in an area that she can get outside daily too to play and go for nature hikes, etc. (you too for the mental break from being a caregiver).
Your mother is fortunate to have you. I'm sure she will appreciate being in her own home and getting to know her granddaughter better.
Best wishes,
Debbie in Maryland