The ideal time is July. The snow has left the low country, but still caps the higher peaks. Wildflower displays are at their best and the weather is usually good. August, too, is good for warm weather. September is the best time to see fall colors, especially the golden larch trees.
Glacier has a number of short kid trails.
Some are even paved or bridged with board walks that are suitable for strollers. Avalanche Creek is one of these. Rain gear is highly recommended on the west side of the divide. Wind gear is highly recommended for the east side of the divide. Search for stores that sell or rent gear near you.