Hi Janice!
Since you mentioned T-Rex in Downtown Disney, did you also consider the Rain Forest Cafe in either Downtown Disney or outside Disney's Animal Kingdom? Both are similar in concept to T-Rex and in fact were developed by the same organization. By the way, the one that borders Disney's Animal Kingdom theme park does not require you to actually go into Animal Kingdom, so you don't have to worry about tickets or anything.
Another great place downtown is
Raglan Road, though I say that from the perspective of an adult as opposed to thinking about where the children might like! However, it really is a wonderful place and in fact, is my favorite eating establishment in Downtown Disney. I recommend looking at the menu over at AllEars.Net and seeing if it would be right for your party.
Finally, it might be nice to visit the Boardwalk area on your first night. There are lots of places to eat there, though my personal favorite is Cape May Cafe in the Beach Club Resort. A place that I have found relatively easy to get into is the Big River Grille at the Boardwalk. It's also relatively easy, in my opinion, to get into the various Table Service restaurants at the Swan and Dolphin. All of these places are an easy walk from the Boardwalk area and there's also generally nighttime entertainment there for the children!
Good luck and write back if you have any more questions!