Is it right/fair or am I being taken advantage of?

I live with my uncle (mother’s side) and aunt (through marriage). I am currently living with them (rent free) with my child (recently turned 5), but I help cook and buy groceries. I moved from out of state and my aunt suggested I stay with them and take care of her mother who has Alzheimer’s. In the beginning, I would cook and clean (full of energy) but now I feel burnt out. They don’t seem to appreciate my help and I feel like I’m being taken advantage of. Here’s why:

Recently, I started asking for days off (one day out of months of consistent working) so I can take care of personal business (daughters doctors appointments mostly and I recently had an important court date). 

I told my aunt two weeks prior the date and time of the court meeting (through text) and she told me that she doesn’t know if she can find someone to look after her mother and that she can not take days off from work so, I might have to take her mother with me.

I tried to change the court date a week before because my aunt had that prior week off but I couldn’t, the lady at court was booked. I informed my aunt and she told me that it was ok, she found someone. The day of court I get up early and get her mother ready for the day, my aunt leaves out for work as I wait for the girl to come. I texted my aunt around the time the girl is suppose to be at the house and my aunt tells me she is not coming because I told her I canceled my meeting and she didn’t even know the date and that I need to communicate better. She then said I can’t leave because I will go to jail. She tells me that I have to take her mother with me, then proceeds to text me 5 mins after getting off the phone saying that she got in contact with the girl and she’s on her way. I was late to my court meeting.

I feel like I’m being taken advantage of because if I have personal things to do in regards to my child (in which I just started asking for a day off here and there, definitely not every month) it should not be my responsibility to take my aunt's mother with me outside. I don’t have a car so when I go out I Uber everywhere and she is in that stage of Alzheimer’s where she poops on herself randomly nor can she walk. I can’t deal with the burden of her and tend to my child at the same time outside.

I also did mention the court date to my uncle and he told me he couldn’t take off of work.

Another thing to consider, I work from 8/8:30am to sometimes 7/7:30pm.

I have no personal time to myself. My daughter is also home with me until she starts school, that is why she has doctors appointments we needed to get her shots up to date. If that is not complete, she will start school late. I feel like no one is trying to help me, yet they said they would. Now it’s just about their needs and wants.