Will GF go to counseling with child to work on their relationship without you? or together the three of you?
If not, have a family meeting, and let everyone have a chance to talk the truth about how they are feeling and how things can improve. Not sure what went down with
CPS but to me the GF has every right to be cautious and not trust child. Trust is very hard to get back. Maybe she can take out daughter 1:1 and have some girl time and work things out?
The age of 13, ugh...lol...it is going to be ups and downs as the next few years are tough on girls. School and friends take over more than family and teen moods are normal but you have to set what is acceptable in your house and what the consequences will be up front so daughter knows what she will gain/loose depending on her behavior. Set up the rules of the house at that family meeting.
Try to plan family time/activities over the next few visits. Good luck!