Unless the child custody order specifically says that the custodial parent is not allowed to move, yes, it's okay for them to move.
I would not have left the child with a stranger either, she is safer at your house until her mother is able to take her back. Whether or not the mother was drinking is irrelevant, since she was not with the child at the time.
Read the child custody order and see exactly what it says; most say "reasonable visitation" for the noncustodial parent. If you want regular visits with the child and cannot agree with the mother about what is reasonable, it will be necessary to go to court and ask the judge to decide. Some courts allow people to represent themselves, and even have booklets explaining how the system works. Call the local court and ask. There are also father's rights organizations that can help, and you can find any local ones by searching the internet.