Nothing personal Rick, but you should get some food service, if not physics knowledge before moving forward.
If you have to heat your toppings at a commissary, get a hot box to transport them in. That will give you a few hours of hold time.
And here’s where the physics comes into play.. Cart has burner. Burner has Flame. Going down the road has wind. Flame and wind not happy campers, unless the flame is in a California forest.
As for the steam pan, which is a pan that holds water between another pan.. Put your dogs in water without a steam bath, will stay hotter and heat up quickly. Condiments such as Chili or Onion sauce would go into a steam pan with a water bath (keeps the stuff from burning)..
Coolers in carts are crap. Heat from the steam table will melt your ice in minutes. Pretty much they’re useless and a waste of space. Keep everything in separate coolers.