Some people aren't going to like what I have to say, but here it is:
You are NOT obligated to take on the responsibility of everyone else's life. These are adults -- and they have to live with the consequences of their own choices. As long as you choose to take care of everybody and not hold them accountable, they will continue to take what they see as the "easy way out" and dump everything onto you.
Get over the martyr complex and declare your independence. Only then will you be able to build a HEALTHY relationship with your family. Until you do, you are "enabling" a whole lot of bad behavior.
File charges for the identity theft. That person committed a crime and the victims (your mom and you) need to stand up for yourselves. If your father doesn't like it, let him pay for any damages. Until he does that, he has no say in the matter. Take a LITTLE time to further assess your mother's situation if need be ... but don't get sucked into giving her the next 10 years of your life. You don't owe her that. Neither do you owe your brothers and your grown children everything you have.
Take care of yourself. Don't donate your whole life to a family that is taking advantage (abusing?) you.