I agree with forshelby - there is something else going on.

I wonder if something has been said to her at her daddy's house about another baby and them being a new family ... or something along those lines. She may "get it" but perhaps she is feeling like she won't be wanted there anymore or that she is not part of "that" family, sort of an "out with the old, in with the new" type feeling??
Maybe also with that being a new family she may think you aren't going to be part of her family any more, does that make sense?
My sister who is 5 years younger than me did the same sort of thing when her mum was having another baby. Clung to dad and didn't want to go home. Just a thought.
Hope you can get to the bottom of it as for forcing her. No, i was forced to visit my mum as a child and i hated every second of it and it made it worse in the long run. Maybe get her dad to call casually a little while before she is supposed to see him and be like "hey X how are you? I miss you i was just wondering if you'd like to come visit?" So it's on her terms and makes her feel special and loved and missed? I don't know... But like i said hope you can sort things out