One thing I'm not seeing much discussed is what Joe's choice to file in Florida and block Sophie from having the kids in England does for Sophie's independence.
By lying about how long the kids lived in Florida to use that state for filing, he's allowed himself to get away with refusing to allow the children to leave without risking much legal issue. So now Sophie has to choose - either she can be with her kids, or she can go home.
He's trapping her in a position where she is away from her family and support networks, as well as limiting her career options, if she wants to be with her children. And if she chooses to go home and not be trapped where he chooses, he can paint her as an absent parent.
He's also forcing a position where his family are easily available to the children but hers aren't, which allows him to claim the children have stronger relationships and support in the US by the time custody hearings roll around.
Rather rich that he and his team are accusing Sophie of trying to force the divorce to the UK to be in her favour, when he's not only hand-picked a state that works in his, but a state that allowed him to use this kind of abusive tactic to get his way.