Not the same situation here, since I'm in a Vee and not a Triad, but would they be amenable to having another type of commitment ceremony that isn't a formal/legal marriage?
P and I are handfasted, as are P and M1. He and I repeat the ceremony each year, and he and M1 do the same. Although we choose to do ours privately, a handfasting ceremony can be just as public as a wedding, should you choose to go that route, and it can actually be tailored for the three of you.
(Obligatory "Check with your lawyer" here, since some states find commitment ceremonies akin to an informal "wedding" and can bag you with anti-polygamy laws... however some states can do the same when a third party cohabitates with a married couple. Something to think about and look into)
Outside of the social difficulties, though, there are other things to consider (and these are things that have made me determine that if P and M1 were to ever get married, I would reevaluate my own relationship with him - it'd be a game-changer).
Legally, if one couple gets married out of the three of you, an imbalance has just been introduced into the dynamic. Regardless of intent now, it would be extremely difficult for me to give M1 that much power over my relationship with P. As an example, we have discussed coming up with Durable Power of Attorney contracts and the like (we haven't actually done it yet), but if P ever married M1 and then ended up in the hospital, and M1 and I had a falling out, I'd bet dollars to donuts that the hospital would refuse me entry, regardless of what paperwork got signed. As the wife, she would have privilege and legal right that I would not have, and that would be an unacceptable imbalance for me.
Note that I'm only speaking for myself here. Others on this board are married and have other partners, and this works well for them, but I'm too damned stubborn and independent to not have this grate on me if I were to try to do the same. (And no, if P were to ask ME to marry him, I'd ask him if he were on crack and refuse, since I wouldn't want to tip the scales in either direction)
The best advice I have for you is to do some soul-searching and figure out what your big worries are if they were to get married, and address those. If you can accept and work with that, then good! If you all compromise and decide a marriage isn't necessary, but a handfasting would be great, then good! If you come to a head and realize you have conflicting goals? Then it's painful, but it's still good. Better to know these things now than ten years down the road. Talk, talk, talk, then talk some more... And see where you go from there. And don't forget to take a break from the heavy stuff and ENJOY your relationship...
Oh, and letting your family dictate when/if you'll get married just leads to them dictating when/if you'll have kids. Stop this madness out of the gate!
(My own mother was adamant that my kids needed a dog, to the point where she introduced the targeted dog to the kids one Christmas with the hopes they'd want to take him home... really? REALLY?!)