Almost have to be the child of people with no brothers or sisters who are also children with no brothers or sisters, or the family has to have super bad luck. 

These include (but are not limited to);a. a drop dead date for her to refinance and take you off the mortgage (5 years, whatever);b. trigger events for her to refinance regardless of date (birth of child, remarriage, failure to maintain the house physically, cease using house as primary residence, failure to pay insurance or property taxes, no "subject to" sales and etc., etc).and no doubt a host of other things.Then there's your remedy if she fails to keep her end of the bargain, including who gets appreciation, right to possess or maintain, etc.Your credit score is far down the list of concerns

My company treats this activity the same (well, almost) as a Child Care (Day care) center, which is a commercial and licensed activity and not appropriate for our leases of single family homes.

Yet, here I am in typical parent fashion, making my first BP post about my child instead of myself.

My wife and I understand that we could give our home to an adult child when we pass away and that our adult child would pay no capital gains taxes on it.But, we have multiple rental properties owned by our LLC and we want to give each our 7 children a property when we pass away.

You need a solution, ask her what that solution is without asking you to stop STR, maybe the petulant child has an acceptable answer in her mind?  

In terms of debts, I agree with @JoeHammel - A title company is the best resource to check on all liens which could be contractor, IRS, bankruptcy, local utility bills or property tax, child support, etc. 

I would think she’s to receive child support payments of a fairly significant amount.  

His wife and child may be moving as well in a few months. 

That last paragraph is the best advice ... consult a specialist.It is possible to structure ownership of a U.S.A. entity such that it is a child (100%) of a Canadian corporation.