Pack some necessities and motivational snacks along the way: backpacks and additional water bottles, toilet paper for going off the trail, bear spray (we didn't see any as this is a pretty busy trail thankfully), trail mix, picnic lunch, rain jackets for all, treats for motivation to get up the mountain (for some this was Skittles, for my son with special needs, it was an iPad turn at the top).
Check the weather for sure and don't do this hike if it is supposed to storm. Even on a partly cloudy day it can sprinkle up on the mountain, so be prepared.
This will take you all day with kids, especially if they happen to be as young as ours or have special needs. It was totally worth it, but it's a strenuous hike, even for adults. Try to get to the trailhead and leave no later than 8:00 a.m. if you are hiking with kids. For adults, the park info says this is a 7-hour hike (10 miles or 16km total) and with younger kids, it took us 9 hours.
This hike would need to happen in milder weather months as the Teton Park Road is closed November through May.