Hello tamana: This appears to be your first post here on PC. So... welcome to PsychCentral... from the Skeezyks!

I hope you find the time you spend here to be of benefit.
Your mum is clearly struggling with her own mental health issues.

I don't know how old you are. But, under any circumstances, you are not responsible for your mum's mental health issues. And it's not your responsibility to try to heal her. (To the extent that anyone is responsible, it is your dad, not you.)
The reality of the situation is that, even if you want to try to heal your mum, you cannot. No one can heal another person. We can each only heal ourselves to the extent that we choose to try to do so. Others can sometimes help us. But we have to make the first move & do the bulk of the work ourselves. If we cannot, or will not, others cannot do it for us.
It is SO unfortunate that your mum is acting what she's acting... guilting you in an effort to make herself feel better about her own lack of self-worth.

You don't deserve this.

Sadly, it has been thrust upon you nevertheless. I'm afraid about all you can do is to try not to take this personally... try not to take it on as being YOUR problem. It's not.
Perhaps you might talk (privately) with your dad about this, if you feel comfortable doing so.

Although from what you wrote it sounds as though talking things over with your dad started some of this to begin with. So you may want to be careful about that too.
If you are still in school, & there is a school counselor available, you might consider talking with that person. And, of course, you can continue posting here on PC.

The important thing is, from my perspective, not to let the emotions you are feeling with regard to this continue to roll around in your mind.

In some way or other, it's important to talk them through with someone in real life, if you can; or at least to perhaps write about them somewhere... here on PC, or in a journal if you keep one... something like that. I wish you well...