...so glad you didn't drop an F-bomb or two. I can relate and I don't even have to be all that mad sometimes. ;)
I think you'll find that there are a lot more places to stop for meals, fuel, and lodging in the West than you think there are. I've done my share of driving throughout the West, including New Mexico and Arizona and I've taken backroads, like mountain roads, whenever possible. I don't believe I've ever gone more than about 40-50 miles without finding restaurants, fuel stations with convenience stores, etc. And even stretches that long are rare. 10-20 miles are probably more typical.But, I noticed some areas, like Montana or New Mexico/Arizona- where I can go hundreds of miles without a place to stop.
I'm currently planning another trip through Washington-Idaho-Montana-South Dakota-Wyoming and I'm avoiding interstates, using several scenic byways out in the boonies, etc. I'm probably going into the less populated areas of some of those states, particularly Montana, and I don't think I have any stretches of more than about 40-50 miles without amenities anywhere along my route.
I think the same can be said for most of the areas in the West. In fact, stretches where there are no road services for over 40-50 miles are rare enough that there are usually signs warning you of that so you can be aware to gas up, etc. before continuing down those roads.
I think you sound like a great mother who is doing her best to have a wonderful trip with your son while, at the same time, being careful to meet his needs. Kudos for that. But I do think that you have a misconception at how spread out services are.
I hope this gives you a bit of piece of mind as you continue your planning.