When I reread all of this, the terminology is a mix, including plural or not. Let's review:
Dad died in 2009. Mom was JTROS?
Mom gave the house to your client. It is not inherited by your client, so there is no step up in basis in 2018 for your client. That's the problem with this type of transfer.
I sure hope this is not in California.
"Level Up" is a gaming function, not a real life function.