There is not a Honda capable of towing your trailer. The Toyota Sequoia SUV or Tundra PU would be at their limit but could do the job. An '01 or '02 Sequoia would be at your $10,000 budget limit. You’d have to install electric brake controllers on these vehicles which will cost about $300.00 more.
Ther are American SUV’s and full sized PU’s that can do the job. You need to get a Ford F-150 with a tow package or F-250 or F-350. This is a big trailer and you need a good sized rig to pull it, with a powerful motor, big brakes, and strong drivettrain to do the job safely.