(SOLVED) movie or TV show in what looks like a post-apocalyptic setting with a Road Warrior style chase

I saw this on TV at least 30 years ago so this movie or TV show must be at least 30 years old. It looked relatively recent, from the 1980s or early 1990s. I watched maybe about 10 minutes of it. It was out in the desert or wilderness somewhere. It looked like it was in a post-apocalyptic setting. One group of people with some sort of vehicles started chasing this other group of people with some sort of vehicles. A guy in the group being chased seemed to be trying to blow fireballs at the chasers. The chasers eventually got the people they were chasing to stop. The chasers were led by a woman. There were some children among the group being chased and after the chase ended one of the children ran up to the woman and bit off one of her fingers.

When I later learned about the Mad Max movies and saw parts of them on TV I developed the assumption that this scene was from one of those movies. But then I did some research and realized it couldn’t have been from one of the Mad Max movies.