Asking the kids for input is a good idea. And another factor might be what areas you can or can't get reservations, unless you plan on winging it.
If you go to Grand Canyon in July, my vote is for north rim. You will see good views (Point Imperial and Cape Royal as well as the North Rim proper) and it will be cooler; besides, south rim would be a whole lotta extra miles.
You might think about taking the boat ride across Jenny Lake and walking back along the south shore (or vice versa). It's pretty and pleasant (unless the weather is bad, of course).
If going to Glacier, you can't tow your trailer across the Sun Road and you're heading west afterward, so maybe you'll want to stay on the west side. Then drive into the park, spend some time around Apgar (stroll the paths, rent a motorboat or canoes for an hour, eat an ice cream cone, or have a picnic) and unwind.
Personally, I like to take my bike just about everyplace. Sometimes there are some nice flat paths to ride and it's a good break from walking (not to mention driving). If the cargo trailer would be too cramped with the bikes, no big deal; otherwise it costs nothing to take them.
If you can have a day of driving followed by a day of mostly walking, exploring, relaxing it can break things up. Driving constantly every day can make the vacation feel like a nonstop vehicular vibrator treatment.