Nanny job from hell

I mainly need to vent- but oh my god I can’t stand my job. I’ve been a nanny for 5 years. For the first 4 years, I was a live in for the same family and it was mostly great. Obviously no situation is perfect, but my day to day with the kids had a good flow and I was happy to be working. I moved to a new city and got a new nanny job for the past year. But it has just gotten worse and worse. My plan has always been to just stay until August, when I will be moving again with my BF and going to college. But I don’t know if I can make it. The situation is it’s a single mum, which I thought would be less difficult as you only have one parent to deal with, but I think she’s actually crazy. She barely works, so she’s home a lot of the time and she caters to every single thing the oldest child wants. She’s three years old, but is the most difficult child I have met. The previous kids I nannied varied in ages but the eldest was 2.5 when I started, and two others were born while I was working for them so I dealt with it all. I know that’s a tough age, but this kid is out of control. What makes it worse, is the mum undermines everything I try to do. For example, today the kid has a fever and runny nose, and the mum told me to take her out in the yard. Fine, I get the kids coat as it’s windy and cold today, and the yard is totally in the shade. The kid tells me she doesn’t want her coat on, I say she needs it as she’s already sick and the mum comes in and says oh no, she’s fine. And takes her outside in the T-shirt, then the mum leaves and the kid is crying she’s too cold and I have to take her inside, she’s red and obviously cold to the touch. I feel like this is causing the kid to ignore everything I say. At lunch time she won’t be super interested in the veggies I give her, but she’s a good eater and she will eat them eventually. But if the mums home and the kid says she doesn’t want to eat it, the mum will give her anything she wants instead, even just ice cream. I get that it’s her kid and if she wants her to eat ice cream for every meal- fine. But she hired me to watch them and has asked me to feed them healthy food only, and now the kid has no respect for me cause she knows if I ask her to do anything she doesn’t want to do, mum will step in and she gets her way and doesn’t have to listen to me. Im just so frustrated and don’t know what to do. I have so much experience doing this, I feel like I deserve a little respect. There’s other stuff that drives me crazy, like the mum leaving all the dishes from the previous night for me to clean. And other small things- but I can’t deal with the kid fighting me all day.