Nothing wrong with OP wanting to keep her paid-for premium seat, even if Mom and kid originally had good seats on a flight cancelled due to the snowstorm.
Nobody ever demanded that I swap seats, but it happened to DH. We were flying back from Denver, and while checking in at the airport kiosk about 90 minutes ahead of time, a screen asked if we'd like to upgrade to First Class for $99 each. We figured, why not? and got separate seats in FC. A guy boarded and ordered DH to move back to coach. Apparently he was a Lifetime Triple Platinum Deluxe Diamond Encrusted Elite, and he wanted his female companion to sit up front with him. He was probably aware that the FC seat next to him was still open earlier in the day, but was too cheap to pay the upgrade for her. A flight attendant denied his command, and he and the woman stormed off the plane raising holy hell. Eventually another person took the guy's FC seat.
(By the way, a 9 page NEW thread!!! I had to look twice to make sure it wasn't a zombie.)