Welcome to the RTA Forum!

The first thing you need to know is that under no circumstances could you ever make this drive in 15 hours. Best case, you're looking at 18-20 hours (likely a bit more considering you're a large group, in a large unstable van where lower speeds are required on the highway and each stop for foods/restrooms/etc will take longer). This is very much two very full days on the road, at the bare minimum.

Do you actually live in San Diego or are you planning to fly there and then start driving to Denver from there? If your plan is to fly to San Diego, I would strongly recommend you rethink your current plan.

I'll be honest, I love a roadtrip, but your plan doesn't sound like one that will be very fun. Sitting in a car all day long for 2 straight days just isn't that much fun, especially not for 4 small children. While there are some great views from the highway, if you want this to be a fun family trip, you need to plan for stops and do things that your children will remember for the right reasons. Your route goes past more than a half dozen National Parks, so there is no shortage of places you could visit to really make this a fun family trip - and not just a grueling drive. However, you'd need more than 2 days to really do that. Right now, I suspect, no one in your family will have much fun, and you're more likely to hate the idea of ever doing a roadtrip again than you will have anything resembling a vacation.

The direct route for this trip is about as simple as it gets: I-15 to I-70. The halfway point is between Cedar City and Beaver, Utah. You should have no trouble finding a hotel that meets your needs in either of those two cities. Those really are your only options to make this a safe trip.