I can’t directly answer your carb count question … but I believe most pizza sauce has a high fructose/sugar count. Checkout the jar labels on the supermarket shelves (though there are some notable exceptions that are worth considering for home-made pizza).
But I just wanted to give you a high five up for “taking one for the team” when the family wants off-the-rack pizza … and NOT eating the crust, which is often the most tempting part You’ve combined love of family with self-control. Noteworthy for you to feel good about!
(Meanwhile, try improving upon those fathead pizza recipes until the family can tolerate the change in taste, i.e., lack of sugary sauce).