Legal Question in Real Estate Law in Illinois

Hard to tell the way you explained it. If YOUR survey shows that YOUR fence is on your neighbor's property and you built the play set up to the fence, yes. You took a risk installing anything in the yard without having your property lines identified for construction purposes. I can't respond to the fence issue as there isn't enough information. But if it is your fence over their line and they are willing to pay to put it where it belongs, this sounds like a fair compromise since otherwise you have to pay for moving the fence too. PS if this is a wood stockade or similar fence with fence sections mounted on posts, there is an easy way to tell whose fence it is: if the fence posts face YOU then the "good side" faces your neighbor, which is correct. The thing is that your neighbor should produce a copy of THEIR survey so you can compare theirs and yours -- sometimes surveyors can be off. And if everything is correct, then you and your neighbor should be able to agree on exactly where the fence should go: the good side should be "on line" so the fence posts are within your property (if that's the kind of fence it is).