I travel with my dogs all the time! One of the first suggestions with a reactive dog is to train him to be calm in whatever carrier/trailer you have. The last thing you want is the embodyment of Rover Road Rage. Place the dog in the carrier/trailer & treat him for calm behavior, then go to the park, and don't ride just let your dog see other dogs passing him by and treat for calm behavior, your dog should soon realize that other dogs are good things, and when they are present good things happen. Once your dog is calm, you start riding (it is not a long process, dogs catch on real quick) and you will soon have a calm traveler. When I travel with one dog (they are small), I use a handlebar carrier, when they both come along I use the trailer.