"for $90k with the remaining $60k considered an equity gift"

"Daughter paid approx $40k down and made several improvements"

"father and daughter "bought" a property together for $150k"

"This was essentially her buying out her dad's portion."

Have you done the math:

She already had $40k+ into it, so his basis share would be roughly $150k minus $40k = $110k. She paid him $90k for something he had $110k into, if you overlook her improvements. Why was there $60k more?

"she ended up selling the home and moving in Oct for $190,000, which on it's surface creates a taxable gain."

Who did she pay the $40k to? Was there always a buy-sell arrangement between them for the future? Who made the payments, insurance, taxes?

"Does the gift, which normally brings it's holding period with it, create a 2+ year ownership period?"

March 2021 sale to her, was deeded/titled?