A.V.
I think that you and your sister need to join forces, decide how you want to treat your mom (respectfully but not enabling) and lay down boundaries that are healthier for yourselves and your children. Honestly, if it's detrimental for your niece to be there - your mom is "sick" and encouraging lazy behaviors in the child - then your sister needs to stand up and find other care. Bryanna is not your mom's child and she needs to back off and be a grandma instead. The more she complains, the more evidence, IMO, that her relationship with the child is more about HER than the kid.
Your dad may argue with you both, and he may have as many codependant issues as she does, but let him argue. Say your piece, and stick with it.
My cousin has fibromyalgia herself and I know she has good days and bad days, but she doesn't act like someone needs to treat her like she's glass. She tells us if the outing is too much and we rest or whatever. She can do a lot on a good day. On a bad day it's enough to just take care of their child.
I think more than anything your mom is controlling and lazy and all these diagnoses give her the excuses she needs. I bet if you look back you'll see that she's always been a touch this or that. You just see it more now.