"I own a mobile home that is over ten years old. The land it is on belongs to someone else. Can the owners of the land force me to move?"
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.