My sitch was the same and I moved because she threatened to move out if I didn't and take the kids with her. Counselor advised I move remarking, "Don't let her take those kids out of that house." Two days after moving out she wanted me to take the kids (to my unfurnished apt) so she could party with OM. A couple of weeks after separating she asked how I would feel about a divorce.
Tell her she can move out since she wants the separation and should pay you what's needed to keep your daughter in that apt. If its common knowledge she's boinking OM tell her she should move in with him (in the kindest and most matter of fact tone possible).
Go for every other week custody (makes sense and is more managable). DO NOT make this easy on her. Think of you and your child FIRST.
You gotta be THE parent, man. First for your D and then the tough love type for your W. Sorry. It's just how it is.
"Fear is the mind-killer" Muad'Dib Me 53, XW 44, DD 14, DS 12 Bomb and OM 12/15/06 Separated 01/02/07 Divorced 05/13/08 X married OM(OMH) 08/2009 Married 06/09/13