I’m a little confused by what you’ve posted. If the HOA documents you were provided when you bought didn’t say anything about a detached playhouse and the structure isn’t visible from the common areas or street, then you should argue that you are not in violation. More than likely the HOA committee knows this, but they probably also know that your complaining neighbor is a PITA, so rather than stand up to him they just send the complaint on to you. If you think any of this is the case, I’d be polite but firm with your argument to the HOA that you are not in violation.
One last thing I will say is that each HOA is different, but one place I lived in had a resident who routinely violated the rules in major ways. He basically just told the HOA to go away (in not so polite words either) and the HOA was never able to really do anything. It even went to court, but the court was fairly sympathetic to arguments that as a homeowner he had rights too.
While I’m not advocating that you fight this legally, know that you do not necessarily need to give in to what the HOA says either.
