Did you have a survey done, and know for a fact that their shed is encroaching on your land?
Did you get Title Insurance when you bought? (Covers you for claims against your title, like that shed).
You also need to consider possible legal consequences from their use of your yard, liability issues, etc.
You could tell your neighbor you will allow this trespass of their shed, and get the agreement in writing and recorded against both properties.
"squatter's laws" ?
***CurrentlyUndone "You're so special and important and gosh, the rest of these Very Mean People don't know what they are talking about. It is so Very Obvious!."
***IsabellaSoriano "...i'm not one for one night stands. not enough time to know if the person is capable of killing me or not. and that scares me most of all. i do not want to be the dumb one watching America's Most Wanted and realizing i slept with the guy on the FBI's top ten list."