You can both contact Social Services and see if they'll allow you supervised contact with the child, but if an order's been made, it must've been for a good reason. The mother should have medical back-up that she's attended a structured anti-drink programme to combat her habit, and it'd go in your favour if you attended an anger management course.
If no charges or cautions were made after the accusations of violence, then I don't see how Social Services can suggest taking the child from the mother if you have contact, but I rather think that the mother needs to prove that she can care for the child in a responsible manner. Only by getting professional help can she show that she's serious about turning her life around. If you're both intent on changing, forget about seeing your child for a while, and see if the relationship's able to progress. If you can get on without abuse, violence and drinking, then at least it's a step forward, but the safety of the child's paramount. Perhaps you could also go on a good parenting course together.