Can you go after the men who fathered your babies for child support?
I don't know your situation but your mother may be really angry and worried for you - you have two children that you can't support. That might make me say somethings I'd regret.
Of course it's not right to be verbally abuse by anyone and i'm sorry that your feeling so depressed because of it.. It would be perfect to get into counseling with your mom to find a better way to communicate as AnnieBrooke mentioned, but even if you can't you could stay away from her as much as possible. I understand that you're being responsible to pay your way, but it would be better to save some money to get out of this situation, and again, the suggestion of moving out with another single mother and kids, may be the answer to your problems. It sounds like you need to upgrade your education so that you can get a better job, and i think that you should be more concerned with that, than paying your way, if your mother doesn't need the rent money that is. You can go to a food bank, to help with the costs of feeding the girls, and use your mother as a baby sitter while you go to school at night, then you wouldn't be in her hair, and she wouldn't be in yours. The less time you spend on fruitless conversations with her the better. Is there anything here that you think might help you right now? I'm sure that the depression will lift somewhat if you get involved in another career direction. That would add some hope and excitement to your life, right?
Sounds like it is time to figure out a way to move, if your mom doesn't see what she is doing. Can you not talk to her about the way she is providing a horrible model for the kids?
What about partnering up with someone else closer to your age, another single mom, and seeing what you can afford together? How stable is your job, and what do you do for daycare?
If daycare is your mom, you might have to find ways to fix (or live with) the criticism and name-calling for a while, until you can get a promotion or better-paying job. Could the two of you see a counselor, just to work out better ways of communication?