Legal Question in Constitutional Law in Texas

Not successfully. Judges are immune from civil liability for actions they take in the course of their duties. The restrained person can challenge the restraining order and/or the subsequent punishment (both of which I presume he opposed in the first place), but that's quite different from trying to hold the judge personally liable.

I'm also not sure how he could show a First Amendment violation. If he didn't ask his relative to write to the petitioner, then how is his freedom of speech -- let alone of the press -- an issue? (Perhaps he relayed the request through another person after learning of the protective order. But the order likely covers such conduct. If it does, and if I'm right about what happened, then the defendant really did violate it.)

Note also that constitutional rights are not absolute. Courts can restrain them in advance under limited circumstances. When a petitioner asks for a restraining order or protective order that would limit the respondent's First Amendment rights, she must show that some of those limited circumstances are present.

The judge in this case must have made such a finding. You've offered no reason to believe the finding was wrong. So your question isn't really about whether the court could make an order restraining the respondent's rights. Instead, it's about whether she could sanction him for violating that order. If the order itself didn't violate his free-speech rights, and if he really did violate it, then punishing him likely would not raise any First Amendment issues.

The judge almost certainly did not believe the version of the facts you've presented to us. She evidently believed the defendant was responsible for his relative's actions. Her belief might be mistaken, but that doesn't mean she did anything improper.

One final point: Even when prior restraints on speech are permitted, there are strict rules about what the restraining / protective order can say. So even if there were grounds to make such an order, it's possible that this particular order was written improperly.

The respondent should consult with a lawyer directly. After learning more about the case, the lawyer should be able to give him some concrete guidance.