How would you handle this

I know I have a lot of silly questions but I want to make the right decisions so here it goes:

I'm joining a new team. I'll be working for a new manager though heirarchially I'll still be under the old manager (who will approve requests and such): the brass who organized the position change will be going on maternity leave any day now.

I asked for a meeting with the new manager I would be under and asked how the transition would work. She said that my old manager said I would be free to work for her full time starting Monday. I immediately found this to be unlikely for a number of reasons including my replacement hasn't been trained enough to do what I do.

I pulled my manager to the side and I was like, "she told me when you agreed to release me to her and that's real soon." My manager's responses was a very diplomatic "tough shite but I need you for longer and I have senority over her."

I obviously want to keep on everyone's good side. I obviously want to accommodate both sides and do the right thing. I know if my boss's boss knew about this, she would rip her a new one and that's bad for a number of reasons including I like her and I will still be reporting to her. But not being able to change positions will only build animosity with the new team and I will fall farther and farther behind in the work that's being done and I'll have a super hard time catching up.

Also, my workload is kinda crazy right now. Definitly struggling as I'm currently trying to look at stuff for both teams.