I have zero idea how being a royal affects things (probably a lot) but I wonder what type of visa he went in with. Was he there as a tourist which severely limits any money making, or some kind of special work visa like the P-2? The Trump administration has recently come down hard on the P-2 which is the one most models, entertainers, etc. use and I believe the one two of his wives used, ironically. The point of that visa seems to be that you have a unique face or talent or whatever and therefore are not taking a job from an American (our daughter who is a model worked in the US with that visa). The fact he is married to an American does not seem to play a major role in the short term as usually you have to apply from outside the US.