I don't think he'll actually understand the move until it is over and done with...he's far too little to fully grasp it all, especially since children absorb our stress (good and bad). No matter how fun it sounds and how involved we allow them to be, its still very scary...its the total unknown for them, its stressful and he's reverting back to wetting as a result.
We as adults tend to get really busy with packing and talking about the move that we forget to still play with our little ones and just sit and talk/hug/cuddle without chatting about the move. You and Daddy are home to him, and as long as you guys are calm and have it under control, he won't care where he's living as long as its with you and he feels a lot of love and attention and his daily routine stays the same. As fun as picking out duplexes are to an adult, its not play, its not cuddle time, and its not the attention he may need, especially at 3...he's still a baby.
Its wonderful that you're trying to include him in the process, but I think its too much for him to absorb. Children are quite egocentric and need constant reassurance that all is well, all is taken care of, and they are loved all the time, especially during times of stress and change. I would try to limit the logistical moving talk to times when he's in bed or busy somewhere else, and focus more on him and keeping things as calm and his routine the same...he doesn't need to be bogged down with adult concepts and moving chaos. He knows its happening, and now all he needs to know is all is taken care of.
If you can have someone watch him the day of the move at a different location, that would be also a good thing for him and you, as you don't need to be having to worry where he is, what he needs or if he's in the way all day. No matter how many people are there to watch him, he's going to want to be with you, and you will be too busy. Maybe he could have a special day for him with someone he loves at a park or children's museum, and then come to the new house once all the chaos has died down? Moving days are stressful for adults and way too much for children under 5 to deal with: hearing people complaining, watching people lug heavy stuff around, watching his old house get empty, his things loaded in a truck, things bumping things around etc. He needs an easy-going day with someone he loves and trusts away from the hectic move, which will also allow him to continue his regular daily routine of lunch, nap, etc. Then, when he comes to the new house at the end of the move and sees you and daddy, you can all talk about plans for his new room and what he did on his special day while you all cuddle and rest. Good luck with it all, and wishing you a happy new home!