Ken, you can't please all of the people all of the time.
If you go all the way from North Lake to South Lake, it is completely a trail hike and you don't get much above 12,000 feet. You have to arrange a car shuttle from end to end, but it isn't very many miles, and with multiple hikers it should not be difficult. Quite a few backpackers use this route.
If you go from North Lake, over Lamarck Col, and back to North Lake, obviously there is no car shuttle. Lamarck Col is about 13,000 feet and is somewhat steep and off-trail, so it is a bit more challenging, even if the total distance is less. The view from Lamarck Col is better, but everybody may be so winded that they can't appreciate it.
Either way, it could be a good trip.