So, your major constraints are:
Dad, 9.5 year old daughter, and 7.5 year old son
Aug 22 - 30th
Flying out of Toronto
Prefers at least one female guide
If you're looking to minimize the cost, I'd suggest you consider <http://ARTA.org>. They are a non-profit, so their prices are a bit less than some of their competitors while, so far as I can tell (I've run two trips with them), their services are quite similar. ARTA runs trips on a few rivers in California, Colorado/Utah, Idaho, and Oregon.
My personal favorite river is the Middle Fork of the Salmon (MFS). It's truly one of the best multi-day wilderness river experiences to easily be had. The Main Salmon is also fine; however, there's a reason I've boated the MFS on the order of 30 times and the Main only 2 or 3. By late August, flows on the Middle Fork are increasingly problematic; most outfitters plan to start flying into a wilderness airstrip 25 miles downstream from the upper put-in for their August launches (although in exceptionally good years, they can "go from the top" well into August. The Middle Fork is spectacular (dropping some 3000 feet from high alpine forest into high desert). The Main Salmon is more subdued, but arguably more kid friendly -- by August it'll offer large sandy beaches perfect for playing on and water well-suited for swimming (in truth, staying cool may be a problem).
ARTA's Main Salmon Newcomer trip launches August 25 and runs $1059/adult (their children's price is typically $999 on the Main); it'd be better if your dates corresponded to their Family trip, but dates are dates. The Middle Fork is more expensive. ARTA has some wonderful female guides and, of late, their regular Main Salmon lead guide has been a woman (but you should confirm that she'll be working your trip). In fact, I just noticed that they've got her picture and bio up at <http://www.arta.org/main-salmon/index.htm>.
Another excellent family-owned outfitter on the Main Salmon is <http://riverguide.com/>. If you talk to the owner ahead of time, he'll often bring one of his daughters (or nowadays his grandchildren) specifically to help with little ones of the trip.
As for the Colorado/Utah options: Gates of Lodore run on the Green and the Yampa River.
The Yampa is mostly free-flowing and the commercials usually stop running it by July 1. It's highly unlikely you'll find a commercial trip there in August.
The Green is dam controlled and will almost certainly be running. At normal flows both this section of the Green and the Yampa are mostly float trips punctuated by very few rapids. The terrain is interesting. But I'd personally try really hard to go to the extra effort to make the Idaho trips (and I say that having boated all 4 runs within the last 2 years (all but Lodore this year)).
I'm not overly familiar with the commercial outfitters in Colorado/Utah; however, I do know that ARTA runs trips there and the same female guide who has been the lead guide for them on the Main for a couple of years was working down there in June. But I don't see any August trips on their calendar.
Blah, blah, blah.
If you're running the Main Salmon, you're probably going to have to pay for the puddle jumper flights. But you might save money by renting a car in Boise, driving it to the "takeout" (McCall for most outfitters), and taking the shuttle flights from there to Salmon.
If you're running the Middle Fork Salmon (in late August), most outfitters will arrange to fly you from Boise to the backcountry strip, and will drop you off at the Salmon airport for the puddle jumper flight back to Boise.
But in both cases above, you can probably get out of paying for 3 people flying 2 relatively expensive puddle jumper trips...
Good luck and have fun,