Adverse possession requires, as a minimum, the following five conditions being met to perfect the title of the disseisor (some jurisdictions further require the possession to be made under a claim of title or a claim of right and/or other requirements listed below):
Actual possession of the property
Open and notorious use of the property
Exclusive use of the property
Hostile or adverse use of the property
Continuous use of the property
see more details at
http://en.wikipedia.org/wiki/Adverse_possession
A lease protects your rights as it establishes that they have permission to use the land (circumventing the "hostile" provision), and also the "exclusive" provision.
If they are not willing to sign a lease, that indicates to me that they have plans that are inconsistent with yours. Let them look it over and if there are any points that are of particular concern to them, bring those back here for some feedback. Tell them that you must discuss it with DH (which you should do) or with your associates or whatever title you wish to give us
Yes, you need to know the process for eviction in your state, although eviction from property is probably not the same as eviction from a residence (and a yurt is portable, and theirs, so they could/should take it with them). Once again, this is more similar to a trailor/mobil home park situation than to a rental house or apartment.