But would the IRS agree since the valuation at the probate action was
$150k and since it was purchased by my mother prior?
The IRS will not agree, but not for the reason you think.
Your father selling the house to you is what is called "related persons transaction". There are very clear rules as to who recognizes the loss, and when.
Assume your father has basis of $250K in the property. He sells it to you, his son, for $100K. I.e.: within your family, without transferring the asset outside of your family's control, you generated a huge $150K loss. It would be reasonable for lawmakers to identify these transactions as a tax evasion scheme and disallow them. Which they did.
So in this scenario (father selling a house with basis of $250K to his son for $100K), the loss of $150K cannot be recognized for taxes. I.e.: father will not deduct the loss on his tax returns. Instead, you (the son) will carry the the loss forward. When you sell the property, you'll deduct that loss from whatever gain you're going to have. Unless you sell it to your son, which would disallow the loss again. You get the picture.
Get back to your scenario: your father has a "stepped-down" basis. I.e.: since the property was owned by his wife, when she passed away he gained control of it as part of the inheritance. His basis is the value at the time of death (or 6 months after). I.e.: in your scenario, father's basis is $150K, not $250K. So by selling to you at FMV - he's not generating any loss at all (which makes things simpler for you since there's no disallowed loss to carry forward until you sell the property).
Talk to a licensed tax adviser (EA/CPA licensed in your State) about the details.