How to deal with my narcissist father and help lessen my mom's pain for being with such a person?

It sounds like you are feeling stuck in this situation.  It seems that there are things that are happening that are beyond your control and you really are struggling with how to manage that.   

I think one of the first steps is really examining what is in your control versus what is beyond your control.  I think often times we spend a lot of energy on focusing things that are beyond our control versus what is in our control.  So in a situation with your dad,  it is important to acknowledge that you have no control over his behavior and that you can only manage how you react to it.   So I think instead of focusing on him, it is important to focus on you.  This is often looking at how you react as well as interact with him. 

It also can be helpful to understand sometimes why people behave in the manner that they do.  Understanding does not mean that you are saying it is ok or accepting it, it just can help you view it sometimes in a different light.  Often times people who are narcissist have over inflated sense of self to over compensate for something.  Often times it is based out of insecurities that they have.  I think also with the control piece it may be linked to a fear that if you go to work or study that means you will leave.  Controlling people so much is often rooted in fear of loosing control, which seems counter intuitive.  I think he also may be fearful of what would happen should you leave the house and see that there are better things out there, this will lessen his ability to control you because your perspectives will/would have changed. 

It sounds like he may not understand that you do not have to leave in order to know that his behavior is not ok, however I think standing up to him and telling him his behavior is not ok is a waste of time and energy because often times true narcissists really lack the ability to be introspective and reflect on their own behavior.   It is also good to remember that you are never responsible for someone else's behavior.  When it feels like no one is good enough for him, try to remember that says way more about him and his struggles than any of you.  It sounds like he may try to put you and your family down to feel better about himself, which unfortunately presents itself in people who struggle with self esteem but do not seek out the tools to address it or fix it, like therapy.

As far as your mom, that is a tough one, I think I would give her the same advice I gave you.  Just to focus on the things that you can control versus the things you cannot.  There is a quote that I refer to when clients are in similar situations "Grant me the serenity to accept the things I cannot change, courage to change the things I can, and the wisdom to know the difference." 

I wish you all the best, I am sorry you are having to manage this but am glad you reached out for help.  I hope what I said was helpful and that there may be a time in the future where it gets better.