"everything that was not in the trust (the house) poured over into the trust."

But that would be only the Parents' ownership. The daughter would become 16% owner and her co-owner now is the Trust. The entire house wasn't the parents' and cannot be put in their trust. That would be stealing 🙂

"as successor trustee of the parents trust dated May 19, 2019, which is nine days prior to the mother's death"

Then Dad didn't own the house at death.

"The house never changed title."

Then the trust is a red herring in this discussion and doesn't apply to that Titled real property at all.

See what's wrong with your analysis? It's all over the place taking everything into consideration, even if it doesn't apply specifically.

"The deed on dad's DOD still read mom, dad, and client as joint tenants."

Then ignore anything about a Trust. The title company was told incorrectly.

You also never told us if this is Joint Tenants Right of Survivorship, or Tenants in Common; community property state?

The Mom died, so her share of the property went wherever it goes in this State relative to the Dad and the Daughter and the deed ownership. If the daughter is considered an Heir along with the Dad, they each got 50% of the Mom's share, for example.

"I think I'm going to assign her 16% (her number) of the basis when purchased 2/27/17 and 16% of the profit less 16% of closing costs and pay capital gains on the difference, unless someone can convince me that's a bad idea."

Send her to a lawyer.