If I did duplex I would have one lease for both units with a stipulation that they had to rent both sides.

Unless you lease stipulates that you have too.  

Dogs) and someone got hurt, then there might be a stipulation in the contract stating you have to cover the costs. 

Unless the mother signed as a guarantor on the lease, in which case the mother IS responsible for unpaid rents, and even damages if the agreement so stipulates.

I probably will not remove any stipulation then he can ask for his non-refundable fee back.

I collected his stipulated payments until he paid off the judgment from his eviction. 

I did stipulate that if another applicant was approved the hold applicant would have the option of signing & securing the lease right away or getting a full refund.

(In Milwaukee judges like what are called "stipulated dismissals" which means that the tenant can work out a payment arrangement with the landlord to pay the past rent, late fees, and attorney/filing fees  to stay in the unit. 

So now we have to stipulate an explicit dollar amount of income, not "3x rent and rent is $1200" - but rather "income must be $3600 minimum".

In this case I would stipulate high late fees, which a tenant shouldn't balk about, because of course they don't ever mean to be late - right?