It is unfortunate you found yourself as 'the other woman ' in this scenario. As he already has along established relationship with this woman it would be wise you file for a formal custody agreement nd soon, also file for child support.make sure all discussions about access are also filed through your solicitor.
Serfdom that there is little you can do. It wasn't a secret as to the type of man he was, but it still sucks. I hope you are able to resolve this with minimum heartache for both you and your daughter.