So...why not sell the gun? (spoilers, quite obviously)
So the guy is so hard up he's trying to sell the car they live in and the camp stove they eat with. But he never thinks pawn the .38 (which is obviously in fine working order) which would probably bring in at least the fifty dollars he was asking for the camp stove and maybe even the hundred he was asking for the car.
Not completely thought out there. You could still do the murder/kidnapping angle by having the guy carjack the dad's car with the kids still inside to make his getaway. Then the dad jumps in front of the car in desperation to save his kids and is run down.