Thank you for your question
My name is Clare
I shall do my best to help you but I need some further information first
What is the problem?
How long have they actually been together?
When the children are in the care of their father it is up to him who they meet and what they do provided he keeps them safe.
It is not unreasonable to ask him not to produce a string of live in girlfriends as this is not safe for them emotionally.
However given they have been together for more than 6 months it is not unreasonable for them to meet her I am afraid.
However if you wish to try and have a clear agreement on these things you can try and arrange to discuss matters with and agree a Parenting Plan using Family mediation
I am sorry not to be able to be more positive about your position - please ask if you need further details