It's kind of like a poll, but with more opinions

I'm wondering what ya'll's thoughts are on God being able to change His mind. Does it happen? Does it not happen? How do you arrive at either conclusion?

Small backstory:

My Dad and I were talking over (and after) dinner the other night and amongst other topics we came to this. He is of the opinion that God does and has changed His mind. For example, the 'adoption' of the Gentiles into the covenant with the Israelites. My Dad's thinking is that up to a certain point, God gave zero cares about what other peoples and tribes did. But then the Israelites kept messing things up and so God changed His mind and decided to include other peoples via Jesus.

Or, as in the case of Sodom and Gomorrah, Abraham argued with God to spare the cities if even one righteous person could be found.

Though I argue that that doesn't count since Lot, a righteous man, was in the city and rather than spare it on his behalf God has the angels get the man the heck out of dodge and then proceeds to get all smite-y anyway.

But I digress.

My thinking is that God, being omniscient, has no reason to change His mind. He knows what's going to happen. He knew before He kick started the whole magilla who was going to do what and when. So there is no 'changing' His mind because this was the plan all along, due to Him knowing what He was doing.

My Dad argues that this is pre-destination.

I say thee nay, since omniscience does not negate free will. Knowing that something will happen does not equal *causing* it to happen.

I can know that if my cat eats too fast she will puke. I know this because, not omniscience, but I have seen her do this her entire life. This doesn't mean I cause it to happen.