Hello clairebear: I see this is your first post here on PC. So... welcome to PsychCentral!

I hope you find PC to be of benefit.
I'm sorry you have experienced so much abuse & sadness in your life.

You asked if you should save this relationship for your children. It's just my personal opinion mind you. But I would say continuing to allow your children to grow up in the environment you describe is itself abusive. You know what being in this relationship has done to you. And you're an adult. Imagine growing up with it from childhood. I suspect your children are going to need a lot of therapy, as it is, to get over the trauma of having lived through this. Continuing to subject them to it is just going to compound the misery, to my way of thinking.
Can you ever overcome the trauma or will it just break you even further? My personal perspective would be there is no way to overcome this trauma as long as you continue to subject yourself & your children to it. Sooner or later it will break you... & probably your children too. Certainly it is possible for both you & your children to heal. But not so long as you remain in this abusive environment I don't believe.
How can you ever trust him again? I personally doubt you can. Your partner needs serious mental health help himself. And you, he & your children need to cut his parents out of your lives permanently, in my opinion. Then, perhaps, healing can begin & renewed trust is possible. But not under the present circumstances I don't believe. And if your partner won't or can't realize he needs serious mental health help then I don't see how any substantive changes can occur.
How can you leave him when he's impaired & can't look after himself? Your first duty, it seems to me, is to your children. Your partner is an adult. And he has to take responsibility for himself. Your children's lives should not be sacrificed to his care needs. He can change if he wants to. He can do the difficult things that must be done to end the abuse & begin to put things right. If he will not it's not for you or your children to sacrifice your futures for him.
I can hardly imagine, I would presume, how excruciatingly difficult this all is, & will likely continue to be for you. Hopefully you can find some help & support for yourself & your children. You mentioned you've seen a psychologist. That's a good start! I don't know if you are continuing to see him. But, from my perspective, I think it would be important to either continue to see him or another mental health professional. Also, if there are any support services available where you live for women escaping abusive relationships, that could perhaps be another important resource for you. I see you live in Australia. I don't know what kinds of services are available to you there. You mentioned your own family along the way in your post. Hopefully they can be of help to you as well.
Here are links to some articles, from PsychCentral's archives, on the subject of abusive relationships & how to escape them, including a quiz you can take to help you come to an understanding of your circumstances:
Recognizing Emotional Abuse | The Recovery Expert
21 Warning Signs of an Emotionally Abusive Relationship
Signs of Emotional Abuse
Are You Trapped In An Abusive Relationship?
Lame Excuses Used to Defend Abusive Behavior | The Exhausted Woman
https://psychcentral.com/blog/how-to...-relationship/
https://blogs.psychcentral.com/recov...e-after-abuse/
https://psychcentral.com/library/domestic_quiz.htm
My best wishes to you & your family...