Especially if the tenants have children.

The third option I imagine is building a completely separate Trust just for the rental property, place the LLC as the beneficiary, along with her children.

This family has four children whereas the previous tenant had none, so it's pretty clear who caused the issue.My lease is clear:Owner will not pay to repair conditions caused by the Tenant, his guest or invitee or damage due to windows or doors left open, sewer/septic stoppages caused by foreign or improper objects in lines, or cosmetic items that do not impact the functionality or use of the item.

Historically, people allowed the home their tenants were living in to get foreclosed on before they let the home where their own children sleep at night get foreclosed on.

We never rent to children, so we should never view tenants or treat tenants as children. 

Meanwhile, my guy's wife and two young children are stuck in a scorching house!

I’d write up a warning letter that dog feces is unacceptable where families and children play and poses a health hazard to the other tenants due to bacteria insects and spreading of disease .

The reason for noting the extra tenants is that their children are now grown, but 3 of them are still living in this 2 bed/1 bath, 1050 sq ft home, with the garage illegally converted to an extra bedroom (allowed by my grandpa originally).So, can we ask them to sign this new Rental Agreement and is there any way to request a security deposit at this point in their Tenancy?

Sorry.There's a plan that can actually work, but it's somewhat of a hassle to implement, Die and have that property go to your children.

This is because they are either accessible by mouth or the surface can create friction/dust or the loose paint can have the paint chips fall/be eaten by children.