I'll never understand why these things even occur in the first place.
When one is spending money to build a lake home, wouldn't you presume they would properly survey and make certain of compliance with setback lines and that construction does not overlap easements? I KNOW that when the title companies act as the disbursing agent for the draws here (next door in WI), they REQUIRE a foundation survey at first or second draw to make certain that no further funds are paid until they verify foundation location is on the correct lot and placed where it does not violate setback lines and easements.
Penny wise pound foolish. So, they saved several hundred bucks by not using proper survey services, now I hope you are able to force them to move the house onto their own land.
Get a RE attorney. NOW! You will also need to obtain a survey establishing the location of the encroachment on YOUR land. They must be forced to remove the encroaching structure. Or buy you a comparable replacement lake lot! This was SO unnecessary.