Protection starts from the moment you purchase insurance. Having travel insurance takes away many stresses and hassles of traveling if something goes wrong.
Before you start booking anything, try to get the kids excited. Talk about Europe with them, read blog posts and books, watch movies and TV shows set in Europe.
For younger kids, you may visit places that aren’t as busy, don’t involve so much walking, and have more younger kid activities.
An optimal time to travel to Europe will be May or September/October when the weather should still be nice, but crowds are fewer as most kids are in school in the USA and Europe.
I know, using points for flights is typically the best value, but why not also use them on accommodation, if it saves you money and is the difference between exploring Europe or staying home.