If that trailer has a dry weight of 10,000 pounds you will likely be near or over 12.000 before you put any bikes or gear in it, let alone tools.
Dry weight usually does not include propane tanks, air conditioners, appliances etc and depending on holding tank size may have 500 pounds of water on board. You should use the gross trailer weight when figuring out how much tongue weight and add that to the weight of the hitch as well as any passengers and cargo you will have in the truck itself. Subtract that amount from the payload capacity of the truck to see if you can carry the weight. Pulling the weight,(max tow weight), is not usually the problem. Payload capacity,(carrying the tongue weight and passengers), almost always runs out first.
