Hmm, I don't think you should worry too much about blasting him away with a switch axe, unless you spam elemental discharge with it, which I strongly recommend not doing so. Damage wise, it's far more efficient to be using the vertical sword mode combo, though the elemental discharge is a great way to end a combo when you have a large window. Exactly what it's meant for, as a deadly finisher. Axe might might be a bit trippy when you do your hack n slash combo, but I don't think you'll be too intrusive unless you're all ganging up on a tiny monster, like the current DLC quests.
A great weapon for grouping would probably be
Sword and Shield (SnS): You can pop lifepowders without having to sheath your weapon (hold R to block, then press the item button, Y), and provide versatile support and sustained damage. If you equip a paralyse sword, you can give your teammates windows of opportunity to pound away at your target, or even make it easier for them to set up deathblow combos or even cut tails. Also, with the addition of mounting, you can abuse SnS's ability to perform jump attacks up or down cliffs to give tons of windows to attack the downed monster.
Hunting Horn: Kinda complex, you can power up your team with your songs and deal pretty decent damage. Most of your attacks will be repetitive, and it can be difficult to land blows against nimble targets. Requires a good deal of practice to utilize properly, but in terms of increasing the damage output of a team, you won't find a stronger alternative. Attack Up (L) adds +15% damage to everyone, and doubling up adds 5% more for a whopping total of +20% damage. Unfortunately, it only lasts 1.5 minutes, increased to 2 with the armor skill "Maestro"
Bowgun. Status, damage, you name it! imo, the hardest to be amazing compared to the others, but if you can master it, you can carry your son anywhere. Downside is in mastering the weapon, you might cause your son to stop playing since he'll have almost nothing to do with you blasting the living daylights out of everything, or even mess up your set up with his interference. But who needs to master it anyways?! We're not looking for 2.5 minute silver rathalos runs, we're looking to have fun with our children!