Thanks everyone. I guess that if SD was showing signs that she was happy to have this contact with her mum we wouldn't be questioning our actions so much. I forgot to mention that since we've allowed mum to be in her life and our lives she's begun to play up a bit at school. Nothing serious, but still a change in behaviour. I guess that's normal though, because she's having contact with her mother who every time she sees her stinks of booze, which just reminds her of the problem.
This situation (not the alcoholism, having mum in our home) is so alien to us I think it's just upset the balance of things and we need to adjust. We will tolerate mum for as long as we need to, because we do need to give SD the opportunity to see her mum before the inevitable happens.