When a borrower is current on the 1st they're behavior becomes more predictable.

We also have a tenant who is a recovering alcoholic and formerly homeless who needed a solid place to get away from family and "friends" that were enabling past behavior.  

Based on the behavior you've described I don't think I'd want her in my rental anyway and would offer her a deal to return the keys and leave, but I wouldn't do this without there being a consequence to her (deposit forfeited, rent paid for the time she's had possession and possibly lease break fee).  

Newbies have no clue as to what is ethical, they don't understand the industry and therefore have no clue as to what acceptable behavior might be.

Every situation is different, so there may be reasons to simply bend over for them, but you are enabling and enforcing their behavior and making all the other landlords out there have to work that much harder to compensate.

You let this go, it becomes learned behavior, and she may start paying whenever you want.That's the principle.  

Is this behavior within the rules of the site?"

Personally I would take care of the repair as a show of good faith and understand that this behavior fosters a good relationship between landlord/tenant.  

That's just more of the same outsourcing behavior that has gotten ou into this situation. 

I don't believe in financially rewarding bad behavior.