Call your lawyer.You should give notice of future rent increases upon possession.

If she's already left the home, there's no need to file for possession.

Since there was a quit claim deed in the chain of possession, and the "ownership" is partitioned, title insurance may be hard to come by.

The non-refundable deposit turns into the security deposit after the move-in inspection and possession takes place.  

If it were me and the tenant does not show up to court, once given the writ of possession I would consider the items abandon and dispose of them. 

Tenant can also say they paid your partner who is no longer the owner as the tenants defense in this situation and can delay your gaining possession of the property.

You have already gained possession, so the payment is on the judgment.

I performed a quiet title action to clear the title and take possession of the property vs having to foreclose.  

So you leave your prized possession of property to the children, and they don't give two hoots about it, and will let it go for pennies!

I'd be more concerned about the hoarding, but again, tenants who are willing to live in C and D neighborhoods tend to overvalue possessions, since replacements or upgrades of said possessions are not in their future.