I haven't done this with young kids, but as a youth leader, I've done about a dozen trips to California from Arizona with a bus load (or two, or three...) of kids ranging in age from 11-18. Also done as a young teen back in the day.
Blythe is always a favorite place to stop because it has all the national fast food joints, but if thats not your style, there are PLENTY of places to stop when you get into California - Palm Springs/Palm Desert is great if you want to stop somewhere a little nicer and let the kiddos get out of the car for a bit. On youth trips we prefer it here because it feels less like a truck stop. We'd eat at places like subway, panda express, rubios, etc. I like to think they are a step above a mcdonalds. Not to put down mcd's, we eat there when we get to Anaheim more than I'd care to admit...

Love that dollar menu!
And if you have the patience to stop for an extended period of time

or love shopping, there is a FAB outlet shopping center with a lot of name brand stores - covering most anyone's favorite. I believe they are called the Cabazon outlets.
We also take the 10 to the 60/91 to the 57. Although when my parents drove as a kid, I think we took that more direct route that someone else mentioned. The drive is boring either way - nothing really to look at until you reach the 57. And then at least there are consistent buildings, houses, greenery! Although by that point I'm so anxious that everything is exciting

I've personally never driven it, but DH has only complained when we drove back home late and night and he was dead tired. The next trip he got a nap in before we left and that made things 100% better!
Also, we leave at 6 AM from north phoenix, and grab chic-fil-a breakfast at the location right at the 101 and the 10. They also have a starbucks and a jamba juice and a couple fast food restaurants. Great start for the trip for us!
Expect traffic as you get nearer to
Disneyland, no matter when you leave or what day it is. It sucks, but for a 6 hour drive to only have about 5.5 hours of traffic isn't bad. Also, if we leave at 6, we arrive by 11:30 am, and thats with a couple stops/bathroom breaks (we love our coffee!). We've done it on both a Thursday and Saturday. We've only ever driven back on Sundays, and its never been a big deal.
Hope that helps!