It all depends on what the majority of the Supreme Court Justices are: Conservatives or Republicans. Trump thinks he has five Republicans. I think he has maybe two. Conservative Justices defend the constitution. When Trump goes to court attacking some constitutional issue like the House's right to investigate, I think he's going to lose.
This is a fundamental flaw in Trump's "us versus them" concept of government. Most people actually have standards and know right from wrong. Some people are sociopaths, but they make up less than 10% of the population. Even Dexter had scruples, and that show was wildly popular. I almost feel sorry for that lawyer who argued in court not to give immigrant kids soap, toothbrushes, and beds. That dead albatross is going to hang around her neck for the rest of her career.