Obviously I don't know your background so don't have a lot to go on here, but I would say that it's really important that you just continue trying to persuade her to go and see her Dad.
If it's only her second visit then it is understandable that she will be a little apprehensive about going, but she is 4 so I am sure she'll be 100% fine once she gets there.
Have you changed your routine much since her Dad left? Or have you tried to stick to a routine as much as possible?
One of my friends had a hard time when her partner left her and started to let bad habits slip into the routine, such as letting herSon stop in her bed at night instead of staying in his own. This ended up causing her all sorts of issues, until she decided enough was enough and started getting strict with him again.
I would say that you just convince her that it will be special Daddy and Daughter time and maybe that will be enough to persuade her it will all be Ok.
Could it be that she is a little jealous because she thinks that her baby sister will be getting all of your attention? Maybe once her sister is going to visit her Dad as well it will become a bit easier and she will be happier about going.
Not sure how much this helps, but hopefully it will. Good luck.