I definitely think there's something going on and thoroughly second the idea of encouraging her to open up to someone she trusts who will listen without putting their own spin on things - whether that's a trusted family friend, school counsellor/chaplain or other relative like grandma etc.

Big family adjustments like a new baby, getting married etc are stressful events for kids and she could easily be feeling a bit insecure and unsure of her place in each family. I don't think forcing her is the way to go, I'd have a quiet talk to Dad without her around and suggest maybe he focus on letting her know how much he enjoys having her around and how important she is to him instead of the "you have to come over" - maybe even make it shorter periods like a day out at the movies or some other activity but she can choose if she wants to stay overnight or go home to your place. Keep reassuring her, keep letting her know that it's ok to talk about how she feels.

The other thought that crosses my mind, as much as it pains me to think it, is much more sinister and has to with the possibility of something having happened to make her afraid of her dad, or spending time at her dad's place. If it is a very sudden change in behaviour, particularly accompanied by other signs like nightmares, bad sleeping, regression etc - please seek out trained help. Places like Relationships Australia have some great advice on getting kids to open up and let you know what's going on that may be able to help.