Wear and tear comes with the territory and some occupants cause more of it than others, regardless of the number of people in the household. 

If I put just one tenant or the other in charge of the lawn, I see them wanting to become territorial about it.Any suggestions on how this could be done?

I am hoping to find a nice location in a US territory in the caribbean and market it as a couples retreat type of deal.

Ca is pretty tricky territory. 

As much as I like pets myself, I know how cats can go around peeing on things to mark their territory,  and how bad that smells, and how dogs can chew or claw trim, and have accidents too, and what an odor pets create when they aren't well groomed.

Or is this dangerous territory in terms of legalities?

While I would rather hold a Pet deposit since they're sure to make their mark one way or the other, if I had a vacancy and a prospective tenant otherwise met the criteria, I'd accept that this goes with the territory of ownership. 

They will spray urine to mark territory.

,You're into "ask your attorney" territory here.

I think we're in a bit of uncharted territory in that this is a health-based crisis (the others weren't), but I firmly believe we'll bounce back from this in the medium to long run.