Before doing this take you wife on a 3 or 4 day ride locally. There are some great roads in the Blue Ridge Mountains and wonderful sights to see in North Carolina and Tennessee. Look up ride reports on this forum posted by forum member Georgiaroller. He has great ride reports that provide inspiration.
The idea is make sure riding for 7 to 10 days at 250 miles per day is something your wife wants to do. This maybe your cup of tea but not hers.
Being in a group maybe detrimental for you and your wife. For instance you'd have to keep up with the group and you may get stuck with people you may or may not get along with. You could find place along the way you want to stay yet the next day you must be another 250 miles down the road.
I have never been riding with a touring company in the US or Canada. Discovery is part of the fun and there is plenty of information on this forum for ride ideas and good times. Most folks on this forum would ride from the east coast to Yellowstone in about 4 days.
I rented a BMW in Arizona for a couple days in Nov 2008 and shipped my gear to the rental place. That worked fine.
If you fly SWA you can pack your gear as 4 bags will fly free. Take you helmets on board. I did last month when I road with forum member Beemberdons.
At 10k for a week or so I presume you are renting a bike. Shipping a bike back and forth would be about $1600 then you could ride your own bike, a bonus indeed. It takes time to learn a new bike and ride it well.
If time is tight rent a bike in Montana. You could get a BMW R1200RT for about $300/day say in
Missoula or rent the bike from EagleRider then go for a ride. Forum members will give you routes and ride ideas and you will have a ball.
Let's see 7 days at $300 a day is $2100 - heck ship your bike to a forum member and save some dough.
By the way I would not go near Yellowstone after the 3rd week in June. It is flipping zoo. Instead go to Glacier National park about the first week of July and ride the Going to the Sun Highway. Then ride to Lake Louise in Canada, then on over to Jasper. Along the way you will ride along Icefield Parkway and have a ball. Also check out riding to the
Hotsprings in BC Canada. Just ride to the different Hotsprings. You can't go wrong.
If you want or need advice on routes I am full if ideas as I have been to many of the good roads in BC.