I think with kids, it is important to try and factor in rest days between your sightseeing and not be too ambitious!
Perhaps with Egypt, you could base yourself in the Sinai peninsula for the beaches and take a 2 day trip to Luxor or Cairo via plane in the middle of your stay?
I would second the Rockies too. Very child friendly, no jabs, perhaps twin centre in Vancouver or Calgary for the stampede, then onto a lodge in the Rockies. We went whale watching, saw bears and elk and messed around in the snow mainly!
You have to be realistic about American national parks. They are nothing like national parks in the UK (with villages, tea rooms, pubs and activities). American national parks are there to preserve wilderness rather than tradition. You really have to make your own fun.
Our last holiday in an American national park was four days in the Smokies (Tennessee). The park was beautiful, but what we did was play in the Cherokee River on the rocks or DH showing off by skimming stones. It was great fun and a really special family time.
The rest of the time we spent at the cheesy attractions in Gatlinburg or Pigeon Forge.
Eastern Europe. Cheap to get to and cheap when you are there. I recommend hiring apartments instead of hotels. They are almost as cheap as camping and having a base with a fridge and a washing machine can't be beaten.
Try Hungary as a starting point. Lake Ballaton is a 2 hour train trip from Budapest and offers nature walks, boating opportunities, wine and culture. Trains in Eastern Europe are quite cheap. DD still waxes lyrical about the overnight train we took from Budapest to Tarnivo in Romania when she was 9.
So far our favourite places have been Slovenia, Hungary and Bulgaria (though keep away from the coast)
Florida keys definitely - my 3 sound like yours only a bit older. they love the outdoors doing stuff even if its just pottering around on a walk or cycle. there is masses to do here - reef snorkelling, glass bottom boat, canoe trips, everglades, fishing, walking/hiking, cycle trails. we will def go back again. the weather is fab too it never goes over 100 so isn't scorchio like the rest of florida can be. pm if you want details of where we stayed etc.
When DD was 9 we went to the Canadian Rockies and for most of the time we were in a motorhome. It was a wonderful experience as we saw great sights and had the fun of fairly cushy camping in some brilliant National Park camp sites. The novelty of Dad chopping up logs to light the fire that we then cooked over is something I am sure she will remember. Oh and we saw bears and elk.
I bet that sort of holiday would work well in the US parks to.
I've taken my DC to lots of places (South Africa, South America, Caribbean, Egypt, L.A, lots of Europe) and we've gone sightseeing and done activities. We've found what works well is to research the country before and each family member gets to choose an activity or place to visit. Also we found avoiding back to back sightseeing works best.We went to Egypt when my DC were 9 and 11 and had a great trip. I wouldn't go during the summer holidays though as very hot for sightseeing. Other holidays that work well are cruises and also twin centre holidays. That way you get a nice balance between busy days and restful days. When my DC were 8 and 10 we had a good holiday in L.A for a few days and then cruised along the Pacific coast of Mexico watching whales as we cruised along. I found travelling works really well with DC that age.
Started thinking about holiday for next year but hit a slight dilemma. There are places that DH and I would like to go, but we think the DC are too young to appreciate them so are thinking we will leave for a year or 2.
Up till now, we've mainly gone self catering or camping in the UK, though a couple of times we've driven to France and self-catered there.
The package holiday, lie by the pool type holiday is probably our worst nightmare - prefer to get out and see places, though do do odd days at the beach because the DC enjoy this.
We'd like to be a bit more adventurous next year, but don't know what would work well with DC of these ages. (If it helps to give an idea of the sort of holiday we'd like to do , DH was thinking about Egypt and American national parks - discounted because of too much sightseeing in the case of Egypt and too much walking in the case of national parks).