I have to disagree with the others. Go THROUGH the trouble is not natural. Going THGOUGH trouble implies an ordeal. If you do something for someone you go TO the trouble. If you're not sure, just google: go to the trouble or to through the trouble.

For North American English, only #2 is natural.

3

Though #3 is fine the sentence sounds smoother in #4. Honestly both work just fine, #3 just sounds more flat

Definitely #4 ! That’s how I’ve heard people say it for years. Unless I’m somehow wrong that’s the correct way to say it ^ ^ you use ‘through’ because it implies a motion or process of things. As if going through a ‘journey’ or ‘various steps’ to come up with the result. “She went through the trouble” Meaning she went out of her way (Put in a lot of effort she didn’t have to) to do this gesture for you. To is more so places and time related. “Let’s GO to” or “It’s TIME to” rather than something that’d fit the context. Though, I’m not an English teacher so this may be poorly worded. I hope this helped :))