The HOA CC&Rs probably didn’t mention playsets specifically, but almost all have clauses that state you can’t modify, construct, or otherwise alter the lot or dwelling exterior without approval from the HOA. That is likely the clause you are violating.
If you are going to do anything to alter your yard or the exterior of your home, give the HOA a quick phone call and see if you need to go through the approval process. That’s what I do and it works well. I haven’t had a problem with my HOA.
To all you piss and moaners telling her how to antagonize her HOA: not a smart move and pretty immature. She bought into the community knowing there were CC&Rs. She apparently misconstrued their application. She should take the time to learn their correct interpretation.