i think either playing as trump or playing as Genie as trump could work
some ideas for Genie pretending to be trump:
Firstly Genie "Lands" on trump when he transports himself to the white-house oval office by accident, killing him wicked witch of the east style
secondly he can't leave the white-house, it's magically insulated for some reason, perhaps you could say there is some magic barrier supposed to keep wizards, witches and stuff out and it's keeping him in instead, could also give a reason why Genie can't just magic her into doing whatever he feels like
third you could then have something like the FBI paranormal department on his ass the whole game, nice parallel between that and the investigation into him and the Russians in the election, also nice X-files tie in if you feel like it, also gives a reason for him not to just magic everything, doesn't want to raise suspicion
either way if we feel like using the husband blackmail to leverage could work, the leverage itself is almost inconsequential, could be using the fact that he's closet gay, a democrat voter, a cross dresser or that he's got a collection of my little pony action figures, should amount to the same thing ie Ivanka being disgusted with him and not having sex with him anymore, that or he could threaten to out that she's screwing justin trudeau on the side, she's then willing to do what it takes to save her marriage.