There are too many issues here - your mum's issue of letting herself get treated badly. Your fathers issues of treating your mother badly and acting immature (and by the way, I think men not going to the doctor is very very common). And there is your issue of wanting a happy family where it may not be possible.

Am afraid that you will not be able to change your parents by yourself. Only they can change but that also means they need to admit some personality flaws and perhaps some therapy. Personally thinking the only thing you can do is help them when you can, when you want to but also not give so much of yourself that you get angry, hurt and resentful. Acceptance that they are less than perfect really helps. Sometimes our parents are less than we hope for, its a real sad thing to have, and it leaves it up to ourselves to make sure we protect our own well-being.

Hugs to you.