Kate -
Grassy Lake Road from Flagg Ranch to Ashton, Idaho is
really not suirable from young kids.
I know the road well - - I used to live in Jackson and continue to live in Wyoming.
And, although it was some time ago, I have ridden it.
It is rough, remote and grueling.
Rocks, por holes, constant up and down.
Once you leave Flagg Ranch there is nothing until you get to Ashton.
And in wet years there is constant mud - this year is a wet year.
https://www.crazyguyonabike.com/doc/page/?o=3d2&page_id=377673&v=5qCommentary from a tour journal -
"As soon as we left pavement, the rocky climbing began. It only took a couple near-wipe-outs to cause us to revert to hike-a-biking. Many times. Disheartening. (Actually, I thought Karen was considering murder.) But eventually, road conditions did improve in many places and we actually rode most of the day ... slowly ... cautiously ... prepared to bail out on moments notice."I am concerned that you and your family do not know what you are getting into.
Plus, if you are from lower elevation, there is the issue of altitude sickness.
You can do excellent loops from both Jenny Lake and Colter Bay.
You can ride up the Gros Ventre River and random camp on the National Forest.
(But you need to know how to camp in grizzly country safely.)
The east side of Grant Teton has many bikeable dirt roads and two track with splendid views.
Plus, there's Snake River Road on the west side of the park close to Jenny Lake.
Jama
PS - Signal Mountain does NOT have hiker/biker sites. Only Jenny Lake and Colter Bay.
All car campgrounds in the region have been reserved long in advance - unlikely to have any openings.