I want to cook some chickens in the morning, and then travel about 2 hours in a car later in the day. Should I cool the chickens in the fridge after cooking them, or just wrap the hot chickens in tin foil and travel with them that way?
This scenario is on the borderline, if the travel time were the only factor. Generally, you don't want to hold foods in the danger zone (40 - 140 F / 8 = 4 - 60 C) more than about 2 hours. However, you have indicated you want to cook the chickens earlier, so that adds on to the time they would not be at a proper temperature if you tried to keep them hot.
The safest method, then, is to chill them properly, and transport them in a cooler packed with ice. Putting the chickens into zip-type bags will keep them from getting water logged.
Using a pre-warmed cooler is a great idea. Many of those ice-packs can actually be heated as well, if you have those type, you can heat them to add more heat to the cooler. I have also used foil wrapped bricks, heated in the oven, and put into the bottom of the cooler (on a trivet or something to prevent the plastic cooler from melting). I also put terry cloth towels on the top to absorb any steam that is given off to keep the mess at a minimum.
If you are going to do this very often, it might be a good idea to invest in a catering front loading food carrier (Cambro makes the one I use). These thermal containers cool down very slowly.