I realize I'm late in this, but this info still holds.
I grew up in Socal and have been camping in JTree for more than 2 decades. Jumbo rocks is deeper in the park, but a better central spot to see all the sites. Cottonwood in the south and Black Rock in the north are the only two places in the park with dump stations. There's a 25ft max TV and TT limit there.
The only two sites I know of where you stand a decent chance of getting any sort of cell signal is Black Rock or Indian Cove. I know IC works for sure because I've used mine there many a time. The rest of the park is a dead zone. But if you want to be out of reach .. it's perfect for that.
They charge for kids? I'm not sure how that is because I've always paid a flat fee for my vehicle regardless of how many ppl are in it. There has always been a 2 tent limit per site tho.
There is BLM land north of JTree/29 palms HWY. I've stayed there once or twice then the monument was full. Not bad but not great either.
Personally my favorite spot to stay in is Jumbo Rocks and occasionally Ryan.