Although narcossees serves "upscale" food, they atmosphere is somewhat casual--not really casual, but the "theme" is seaside restaurant, so there are simple navy tablecloths and wood floors. It's a very comfortable place to take children, especially because it gets pretty loud in there with the open kitchen and wood floors! (drowns out the kids pretty good)lol
Yachtsman is kind of the same way--lots of lighter colored wood--it gave me a somewhat casual feel compared to say, Citricos. Wooden chairs, wooden floor, that kind of thing. I am sure you will fine at both places with children. After all, it is WDW, and children and families are welcome.
Besides, you have to get your kids used to eating in nicer restaurants someday, if not now, when? I am sure you want them to learn how to behave in places like that, and we've all been there with our kids, so most folks are pretty understanding as long as you take them out before they "swing from the chandeliers" as someone said upthread!