If you do choose to allow them to keep the animals I would amend the lease with clauses addressing the pets, charge deposits, and require that the tenants show proof of renters insurance covering the animals if they would cause harm to anyone.

@Malik Batchelor I would suggest getting the Driving for dollars App for $20 bucks a month and save yourself a TON of time and just input the address and save it to a list you build on the APP and then BOOM there is all the owner contact info with even a Phone number.

I need help on how to address this!

You mentioned probate, did she die without will/trust, that matters as to who inherits and many legal and tax consequences.

He also feels that I need to wait until the job is done and trust him, but according to the two realtors (they know investment properties really well), this is a bad flip.

Don't trust anything unless it is on a government website or from a lawyer. 

I have learned over the years to trust the recommendation of the background check.

She is not trust worthy and clearly can not afford the rent.

You'll also need to gain their trust which will be difficult if you don't have a track record and aren't putting much of your own money in the deal.

My older brother is an attorney in our hometown, and has a fledlging practice specializing in estates, trusts, and wills.