Can you at least provide the area you live in, is it a large city, small town? Since the mother beat the minor, the mother should be reported to CPS or to the police. I know emergency assistance is available in dire circumstances, but I don't know where to point you because I don't even have a clear idea where you live. Three people can get by on the food normally consumed by 2 people. It' s far healthier than allowing the 16 year old to go without any food. She's still growing, your not, and I remember what it's like to fill up on ramen noodles and peanut butter between paychecks.
Life hasn't treated this young woman very well, you think you can't stretch the money you currently bring in??? You can, it takes some discipline, but it can be done.