I don't know how old your mother is...but to be open with you...because of a divorce, I wound up with no place to live, no car, and not able to work. I just turned 62 this year, and have low income based housing (and free wifi). I only get social security. I have kids..none were in a position to help me.
And I am not alcoholic...so I think there are programs that I would not qualify for.
Think of it this way..what if your mom HAD no children? what would she do then? I know it is stressing you, but you HAVE TO THINK of your child first. And not let others make you feel guilty for knowing this truth.
The alcoholism is something she has to take ownership of...and go from there. That's the hard reality I am learning here, based on a boyfriend who is alcoholic. I probably am pretty close to calling that an ex boyfriend...