Moving and cant find a way to transport children in the car i have?

Okay I'm trying to do a long distance move Texas to NH with dog cat and two kids....i have a ford explorer sport most ideal way to move would be a cargo trailer but uhaul (or any other company) doesn't seem to support it.I cant get a truck and tow mine because i have two children in car seats and you cant use car seats in the truck, other option is moving company or pod but they want 2000-3000 which seems unreal when i was looking at less then 500 to get the cargo trailer. Any ideas it would be a big help.