My thoughts on your post - well you did ask
Having ridden Canada to Patagonia recently I would say 3 months is not long enough for such a trip to catch your breath and look around.
Alaska is beautiful wilderness and I love that stuff now but when I was a younger traveller I wanted a bit of life and culture.
So I reckon a combination of wilderness, culture/action, exotic destination and holiday time would make the perfect first trip for a family - something for everyone.
My option would be ride down the Appalachian MABDR (wilderness plus lots of iconic routes such as Skyway, dragons tail etc), down to New Orleans (culture), then down into Mexico (exotic) If you go down the east side (not the coast) you’ll come across very few non-Mexican tourists and be in the real Mexico. There are beautiful mountains with waterfalls and Cenotes without the crowds. head down to Oaxaca for food and cool beaches then if you still want a bit of main steam holiday head for Yucatan.
Back via the west route - I’m sure I don’t have to list the stuff to see on the way back.
If I hadn’t already done most of this I’d be planning a trip now 
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