We have a 2009 Edge as my husband's primary car. I think it is a great car, and has plenty of room. We only have one child (17 months), but I think it would definitely be enough room for 2 children with 2 full car seats in the back. The person sitting in the center though would have to be tiny though.
I disagree on one post about interior space. We have a rear facing car seat in the back seat passenger side, and we don't have to sacrifice leg room in the front, even for a taller person. I've also sat in the back for extended car rides, and there is plenty of leg room even behind the driver's seat. The cargo space is very good and large - I think that you would just have to pack smart and eliminate super large strollers or objects that are cumbersome.
I haven't seen a Traverse, but my guess is that if you have a 3rd row of seats, you're going to sacrifice cargo space. So you have to weigh the trade-off.
The only thing negative I have about the Edge is that I have a hard time with the blind spots. Yes, there are small blind spot mirrors on the side mirrors to help, but I still have the habit of looking back over my shoulder. In this car, I have to strain backwards to see the blind spot clearly, and sometimes can't see it well at all. But I prefer to drive sedans and smaller cars, so that may contribute. The Edge does seem a bit big for me though to want to drive it on a regular basis.
Best of luck to you!