Great supportive fathering, there. Sheesh.
I went to new daycare after my parents were divorced and we moved to a new state (age 4 or so), so lots of transitions, and I remember crying at dropoff for what seemed like months. The teachers were totally unsympathetic - made me sit in the corner because I wouldn't stop. Mocked me in front of the class for coloring my snowman green. Not that I'm scarred or anything, heh.
Anyway, the point of that trip down memory lane is that transitions are really hard for kids. It sounds like there is tension at home, and now this whole new daycare, which is all very stressful for a child. She has zero control over what happens in her life - she can't stop her parents from fighting (or whatever) and can't stop her daycare from changing. In your position, I would do whatever I could to help her feel a little bit in control. I'm not sure what your options are, but I think taking her to work with you for one day wasn't a bad idea to show that you're trying to help. Is this daycare just temporary until fall? If yes, would you consider a nanny for a few weeks, maybe a college student or something like that to help with the transition to kindergarten? Is there a family member who can help temporarily?
I can't say what the solution is, but I encourage you to keep trying for creative ideas; listen to her and try to get to the bottom of things. (and tell her father that YES SHE WILL HOLD IT AGAINST HIM LATER. ;-)