I don’t envy you. I’ve made that trip several times and it’s no fun. Places to stop along the way include:
Dorris ave exit (it might mention Lemoore or Hanford I can’t remember) has several places to eat including a fosters freeze and a restaurant call the apricot tree
Kettelman city: They have an In-n-Out that is always busy but the bathrooms are usually pretty clean (compared to other places along I-5) and if you need to top off your tank there are several gas stations (the furthest one from the freeway - on the left - is usually the cheapest)
Buttonwillow (Mc Kittric Hwy) has a large travel center. Great for gas, road snacks and bathrooms
After the 99 merge there is a little “town” called Grapevine (it’s just before you start going up “the grapevine” into the hills) If you’re tired, and you probably will be, there is a motel there (I think it’s a ramada) they have a good breakfast bar in the morning and give a AAA discount
Going through the hills the cheap gas is at Fraizer Mtn Prkwy. The lowest price goes back and forth between the Flying J and the ARCO.
The Castaic/Santa Clarita area has tons of places to stop and is your first chance to go to a real grocery store on your trip. Its in Castaic. You’ll take the Lake Huges Rd exit, go under the freeway and make a left at Castaic rd. The shopping center will be on your rt. There’s a starbucks a bank and an Albertsons in the back.
Once you come out of the hills you’ll be in the lovely San Fernando Valley (that was sarcasm) I lived there for a year and it is easily one of the top 5 hottest most miserable places on earth (or at least in CA). So crank up your AC going trough there. Since I don’t know where you’re going from there (I-5 toward Disneyland or 405 to Orange county and San Diego) I’ll stop with the directions. If you need any more info feel free to send me a personal message. I lived in LA and San Diego for several years after college. Oh and as for places to let the kids run and get out some energy I would probably stick with the freeway rest stops. They usually have some shade and area to run free (and some of them now have WiFi). When my parents took me to DisneyLand when I was 5 we stopped at the rest area just before Buttonwillow for a picnic it’s definitely one of the bigger/nicer rest areas.
You may also want to consider taking 99 down if your kids tend to need lots of stops. It will make you trip a bit longer but you will have more options for stopping.
Have a safe trip,
Oh and skip 101. Yes it's beutiful (I went to college in San Luis Obispo) but it takes forever and is not with out it's fare share of backups (Santa Barbara can be a real nightmare.)