What do you mean they can’t prove it. So if there were welts and bruises, who the police said inflicted them on a child? It happened more than once? The lawyer told you to stay with a violent man? What???

Take yourself to domestic abuse shelter. They’ll help you. Longer you stay worse it will get. “Stay at home mom” is not an excuse for subjecting your child to abuse. Call child protective service and call domestic abuse shelter. They’ll come and get you and support you through getting on your feet