Evicting a family member living in their trailer or other vehicle on your property is the same as any other eviction. If the trailer is theirs, they must take it when leaving. If they do not, you must keep it as your state laws require. If you want to claim it, your state laws for claiming and retitling abandoned vehicles explain how to do this. Discuss this with an attorney before "claiming" an abandoned trailer. There are strict abandonment and salvage laws in each state, and your relative could reclaim the vehicle as stolen if you're not careful.