Hi, Jill! With the exception of some of the Signature Restaurants, most dining locations at WDW are kid friendly in both the menu selection and the overall atmosphere. I took 4 kids under the age of 8 to the Yachtsman Steakhouse at the Yacht Club last year, and although upscale and more "adult" in my opinion, the cast members could not have been kinder to the kids and made them feel very welcome.
My only advice to you is to make sure to have advance dining reservations for your group. With little ones, you are best off with a plan and not having to wait around for a table. You can make reservations online or by calling (407)WDW-DINE. You might also want to go to
www.allears.net and select DINING where you can find menus for each location to make sure the menu appeals to you.
And, while all will be appropriate, count on Chef Mickey's being a bit hit with your 2 year olds (and the adults will love the dessert table - one of my favorites!) Have a great time!