Not sure when you are going, so I will assume it will be summer. Crater of Diamonds SP is less than 2 hours SW of Little Rock, and the campground has been renovated and has full hookups and lots of trees. We did not have a toad, so we simply walked the path to the entrance to the diamond fields (took maybe 10 minutes). There is also a water park inside the park, and kids were having a blast. It is a small water park, but nicely done. Check out the link, we found several small diamonds, and someone found a large diamond everyday we were there (5 days total).
We only spent one day in Hot Springs, and there are lots of CG's with pools and things for kids to do. We made reservations for the SP, and will definitely go back someday.
Diamond Mines - Crater of Diamonds State Park
Along I-40 near Amarillo is Palo Duro Canyon SP, simply amazing! Check out the link for all the activities for the kids.
Palo Duro Canyon State Park — Texas Parks & Wildlife Department
The only other advice I have to offer is if you need a kid friendly CG near Albuquerque, American RV Park is on the far west end of town, and they have a pool and hot tub, along with free breakfast.
American RV Park
Have fun! Holler if I answer any questions.