We tend to spend 2 whole days just at Epcot. My kids love it and always have, even when they were 1 1/2 and 5.
I think 1 day is doable, though. It helps that Futureworld is open earlier than WS and would be even better if you could do this on an EMH day. Hit the park at rope drop. If the kids meet the height requirements, I would plan on riding Soarin', and Test Track for sure.
This is the order I would do Futureworld.
Soarin'
Living With the Land
The Seas with Nemo and Friends (My kids always want to do Turtle Talk with Crush after this)
Test Track
Journey into Imagination
(If you have time, the kids are probably going to want to linger in some of these pavilions after you get off rides, like The Seas and Imagination Pavilions.)
We haven't lingered too much in the Innoventions buildings the last couple of visits. Don't really know why since there is plenty to do in there.
For World Showcase, there is no way you can adequately cover every single country in one day. You can, however, visit each one briefly. One year, we flew through each country so my MIL could "see" each one, since it was her last day. The kids were so focused on getting their Kidcot masks stamped. It wasn't fun for us. We prefer to pick a few and spend more quality time in those particular countries. Our favorites are Norway, United Kingdom, Japan, Morocco, France, American Adventure and Germany. Okay, so that's more than a few.
In the past, we have saved Spaceship Earth for our very last attraction. Sometimes we watch Illuminations, sometimes not. It depends on how the kids are feeling by then. It is very loud and my kids have sensory issues with noise.