Our ex was like that too. She no longer has to be like this as SD (14) clearly sees coming to our house as an EOW event, not one day more, not on vacation, not when she's home-schooling, not even to go on vacation to her home country with us.
When she was 9, she would spend 50% of the time with us in the summer (1 week at a time). The mother got a cleaning job nearby on Wednesdays, she would come visit her, totally ignore me in my own house.
During the rest of the year, when SD would be with us EOW (Friday night to Sunday afternoon), she would always find a reason to call.
My DP does go to her house to visit SD the weekends she's not with us.
I remember I once went to pick up SD for literally one(!) day, she was almost 13, the mother took off to McDonald's telling my DP that I had to go there. They saw me in the parking lot, she came out with SD and stood there hugging for a few minutes.
My DP doesn't see an issue there because the mother has the right to hug and miss the kids. I know it's subtle manipulation to make sure that the child prefers the mother, but it's hard to prove. To be honest, I don't think there's anything that can be done about it, other than ignoring and concentrating on other things. I limit my involvement with SD to the minimum, I have my own kids to take care of.