You cannot expect these people to treat you well when you don’t treat yourself well. It sounds and though you’ve got into a family pattern of you being the giver and them being the taker. The more you give, the more they expect you to give and the more unreasonable they will think you are by not giving however unreasonable their demands actually are. You have also chosen a partner, who is a taker. That’s not surprising as you are a giver.
If you want things to change, that is actually really really hard. I only changed due to illness. Then got therapy. It’s going to be scary for you. But if you don’t do it, you’re going to get ill too. The most important person in your life is you. Rather like on a plane, you put your oxygen mask on first, you can only look after others when you are ok yourself.
I agree with others. You need to stop saying yes. You enjoy looking after the baby. But you agreed half the time. Would you still be ok with this or would you prefer once a week or just from time to time? Your sister doesn’t seem to have a problem with her in laws not helping out. So why should she have a problem with you not doing so? Well, she will obviously. But you see what I’m getting at, don’t you? Decide what you want to do. Give a deadline for her to find alternative care and stick to it. She loses her job? Not your problem.
As for your dad. You’re not his slave. Why on earth is he living with you? He enjoys your mums company. Maybe he should be living there. Or with your sister. Or maybe, newsflash, standing on his own two feet. Does he pay his way, rent/ bills etc?
As for your partner, in for a penny, in for a pound. What pleasure does he give you in life? Are you with him for love or habit?
I think you could do with some rl support. I’d not be going to your mum for this either. She’s pally with your dad. Maybe you can take some of the free time you’ll have by not taking the baby to spend time doing things you enjoy or getting some therapy of your own.