If you openly and notoriously use land that belongs to someone else, e.g., build a garage or driveway that covers part of a neighbor's land, after some period of time the law will preclude that other landowner from disturbing your use of the property you've been using. This is called "adverse possession". The rules differ considerably by state so you always need to hire a local real estate attorney familiar with state law. The rules may differ as to the existence and nature of this right, how long and to what degree you have to use the other person's property, and what process you have to go through if any to confirm your ownership (title) to the property you adversely possessed.

Your situation raises another issue in addition to the above. Can placing a mobile home on property, something that is inherently movable and not permanent, ever arise to the level of adverse possession? If you had build a permanent structure the argument would be clearly stronger. It is not clear whether or not a mobile home will suffice. It might even turn on whether you first built a foundation (e.g., concrete pad) on which you placed the mobile home and whether you, or the owner, had added permanent plumbing lines to the mobile home.

Bottom line, hire a local real estate attorney to sort these issues out for you.