Every signature restaurant at WDW will have kids in it. As long as they are well behaved, of course, they are always welcome, and people should expect them to be there. (exception of course, for Victoria and Alberts)
I would suggest you try Narcoosees. It is a slightly more casual vibe there and with the wood floor and high ceiling it has a slightly louder noise level there as well, so kids are less noticeable if getting a bit fidgety. Really, your kids are welcome anywhere, so choose whatever restaurant you wish to dine in. Bring some things to keep them busy, the kid menus and crayons they offer wear off quick. Maybe pick up another coloring book from a resort gift shop or some stickers or something before you go. I think it's great you are taking the young ones to a nicer place to dine, as they get older they will have learned how to behave by learning it young, you know?
Artist Point is another good choice as the tables are not too close together, and it also has a very high ceiling. Narcoosees windows have a better view for the kids though.