I totally agree with Artechim too

Have you considered re-evaluating the living situation - perhaps now is the right time for her to be with her Mum, in 3-4 years she will be a young woman (girls grow up so quickly these days) and you risk leaving it too late. By making time for a newborn and not your 9yo in your busy life you are sending your 9 year old a very strong message Simply, I guess from the outside looking in it seems you are prepared to make room in your life for a new child you don't even have yet instead of the one you do.

Just trying to let you consider a totally different perspective on the situation - your 9yo is probably wondering about some of these things