That trip sounds brutal to me
We generally recommend not traveling more than 500-550 miles per day. However, this does not apply to trips when you're towing a trailer or when you have kids. You have both issues. I would say that 400 miles per day would be about the most you could comfortably do without it being a slog of marathon proportions. Having done my share of trips with kids and with both a truck/camper and truck/trailer combo, I really think even 400 miles per day is pushing it just due to the reduced speed and maneuverability.
Even if you take out all the side-trips, you're looking at almost 3600 miles, and still 9 days of traveling.
If you need to get to San Antonio, this is a situation where flying makes more sense. Or you need to add days.