If you use the damage deposit from a listing site, and they deny the damage, you may get nothing.

Quote from @Samuel Mutschler: This is mental illness, substance abuse, or someone trying to get out of their lease.I would tell them the rental is unsafe and they should leave.

Hopefully you have other, better qualified applicants to go with or can deny this couple on something else (credit, income) so you don't have to deal with their nonsense.

And we take a bus and see several properties with the builder. 

Generally a tenant cannot deny you entry to fix a problem.

Denying application because of pet is not about discrimination (man they abused this word so much), it's about who pays for the cleanup cost.

Quote from @Dan Denis: Is building better than buying ? 

We know we could apply for a zoning change, but that process could/would take months and we are beyond ready to move onto our next investment.Has anyone else come across problems like this, where the lender is going down a rabbit hole and denying funds because of something that could possibly happen in the future?

Look up the situation the rapper Killer Mike went through when he attempted and was denied…it’s crazy he didn’t get approved cause his situation was BAD) so the fact that she was able to successfully do it meant that she was in serious, dire straits.

Of course, some folks have abused that provision in the law.