It's not really that LAX is hectic, it's just crowded and EVERYTHING takes forever. Baggage takes 45 min on average to come out on the carousel. Waiting on transportation shuttles takes a long time. Getting to the rental cars takes a long time. Security lines are always horrendous. It's a function of the layout of the airport combined with the endless construction happening there.
So, what you need is patience, and just know that nothing will happen quickly or efficiently.
I have 2 autistic kids so here is my advice.
If one adult and one kid (the 8 year old, or the 10 year old if he is a "helper" type like my oldest autistic son or both) can handle the luggage, have them stay behind at the carousel while the other parent goes ahead to the rental car place. Once luggage is acquired, GO TO THE RENTAL CAR PLACE TO MEET THE OTHER PARENT. Under no circumstances should the rental car driver return to the terminal. Meet at the rental car. Have the one picking up the car text the stall number and vehicle type so they can be found. This will take the least amount of time and cut down on trying to keep a large group together in a crowded situation.
Now, if your kids will need boosters, just rent them through the rental car agency so they will be ready to go when you get the car. Or, bring something inflatable like a bubble bum seat that can be carried in a carryon bag.
Do NOT plan to eat at the airport. Since you arrive at a good time, traffic wise, just plan to stop somewhere on the way to DL (I'd recommend In n Out). Or, simply pack lunch and eat on the plane. Something easy like sandwiches and fruit.