A lot of good advice from those that have hiked in the canyon. It has its own set of difficulties, heat, lack of water, steep descent and ascent, easier when hiking down, more difficult when tired while hiking up which is opposite to mountain hiking.
There are families who backpack in the canyon so it is doable but they are probably very experienced and very hiking fit. If you do a search, I think there are forums dedicated to hiking/backpacking in the GC and you may find better info to help you decide on your own situation regarding young family backpacking.
I would recommend day hiking part way down on the 2 corridor trails, Bright Angel and South Kaibab. Great views and you could gauge how ready your family is for what you are planning. The GC is spectacular and worth the effort of a hiking trip. It will always be there in the future if you think this is not the right time for the whole family to backpack to the river and back at this time.
Dave
Dave