First - welcome to the site! Many good points above. Although many might seem to be somewhat negative, I believe that it's really a matter of people trying to be helpful by pointing out the difficulties in what you propose to do. It's all great information from very experienced people. I hunt primarily alone (but with a dog), so when my dog was sitting out for a year due to injury, I had to hunt completely alone. I did not have a whole lot of success, but I did have lots of fun. You will have the added advantage of two more sets of boots to stomp around and intercept, agitate, flush birds, and also two more sets of eyes to see them fall, and find them. I apologise if the following lists repeats some of what was said above - but consider it another "vote" for that method/tip!
1. Go quietly and slowly, and stop often. Tell your party ahead of time that you will all stop together, and that you will all be very quiet when you stop (minimal chatter - do your talkin' while you're walkin'!). The key to this is that the bird heard you coming, and got a little freaked out, and now that you are silent he doesn't know where you are, and that freaks him out - time to fly! If you keep talking he'll still know where you are, and might be more likely to use that information to evade you. Personally, I walk 5 steps, then stop for a long 10-count. It takes forever to get anywhere, but it's effective. Be prepared for heart-stopping flushes - it was one of my favourite aspects of huntign without a dog was that you never knew when a flush would scare the bejeebers outta you!
2. Agree with your party that anyone who has a shot at the bird will take the shot, even if the other person is too. Pheasants are hard to kill, and I can't agree enough with the concerns above about lost cripples. Even WITH a good dog, they can be hard to find. Without one, your likelihood of finding a crippled bird is exceedingly low. Can't stress this one enough. So although it might be less satisfying if two guns shoot the same bird, and they might get a little banged up, it will be less upsetting that losing birds that you knock down, especially with your son along - I'm sure you want to set a good example about the importance of retrieving downed game.
3. On a related note - good advice above about taking the time to visually 'mark' the fall of the bird. There will be time for high-fives later, once you find it. Given that you are three - maybe one person stays where they were to direct the other two to where the bird fell. Then mark that spot and the three of you can search.
4. Strategically, blocking is a great idea, especially if you have some kind of linear habitat feature like a ditch or edge of some kind. If it's square, why not try a shooter on the corner and one pusher coming down each edge towards the corner, each swinging out into the cover.
5. Choke tubes. The year that I hunted wihtout a dog I put IM/Full tubes in my shotgun (compared to an IC and M when with the dog). My idea wiht that would be that it would increase my chances of either a clean miss or a thorough kill. A bit like my point above about tag-team shooting, it might bang up the birds a bit, but in my opinion "A banged-up bird in the vest is worth two suffering crippled that crawled into a hole"! I used #4.
Have fun, be careful and most importantly, make sure to come back here and post a few pics of the happy family excursion - with birds or without!
Cheers,
-Croc