after towing a trailer(running lights not working on trailer) after I cut off my truck,then…
CAR IS SKIPPING AND ALTHOUGH THE ENGINE IS NOT GETTING HOT THE UNDERSIDE OF THE CAR GETS SO HOT IT SMOKES
The smoke is just an indication of a fluid leak. You can check your fluid levels periodically to determine which fluid level is getting low. This is the fluid that is leaking.
If the check engine light is on it may have a code that will help diagnose the cause of the skipping. The good news is just about any local auto parts store will pull the codes for free. Once you have the code post them and I can give you the right information.