Everything you can come up with as a "solution" is really just a stop gap measure. Instead of specifying the style by name, you could specify it by example image. Instead of training the AI on her images directly, you could train a second generation AI on images drawn in that style generated by another AI that was trained on her images. Thus your second generation AI would be free of any copyrighted work. And of course the whole copyright thing only comes into play when people redistribute the AI. If AI is easy to train yourself locally, even that doesn't matter anymore.
If you want to go all Butlerian Jihad on the world, you might be able to stop it. As long as AI is allowed, this ain't going away, it's only getting easier, cheaper and faster.