Best all in one solution is going to be a new full size SUV. It will fit inside the garage, carry your children and their stuff, and tow the trailer. You can save a lot by buying a used SUV, in particular one that is coming off a lease and is going to be 2-3 years old and with 30,000 or fewer miles on it. Look for one that came from the factory with the tow package option. You can lookup the vehicles VIN to confirm what was provided at the factory.
Gas economy will not be as good as with a pickup or your MDX but in terms of total costs for everything auto related it is the least important factor. If you have a truck only for towing you need to consider where you will keep it and some maintenance is required whether the truck is driven or not an in general it is harder on a vehicle that is sitting in terms of problems with the oil, fuel, AC compressor seals, tires, etc.