My husband and I are also mid-20's and just returned from our May 8-15 stay. Here is what I remember from the restaurants we chose, in regards to kids:
1. Tony's Town Square - 6:30 seating, saw only a couple of children and no melt downs. Perhaps b/c of the semi-early seating? Not a place I would recommend though, based on the food. Our least favorite of the trip.
2. Teppan Edo - 7:30 seating, we were sat at a table with a family that had 3 children. They behaved fairly well, maybe due to the entertainment of the grill in front of them. We loved this place for the food.
3. California Grill - 7:30 seating, saw only one family with kids and they were fine. We didn't do a late seating for Wishes so I don't know how it would have been later. Best meal of the trip.
4. Boma breakfast - lots of families with kids but they all seemed fine to me...but it was also early. Great breakfast.
5. Whispering Canyon Cafe - 7:30 seating, of course there were lots of kids at this restaurant. It was fairly loud and fun. If you want to escape this type of atmosphere I would not recommend for you. But we did enjoy our experience very much.
6. Kona Cafe - 7:30 seating, we were seated in a corner by another couple. I don't even recall there being kids in this restaurant, although I'm sure there were. Great food.
7. Le Cellier - 8:15 seating, we were next to another young couple to one side and then a mother with her 8-9yo son on the other. He was very quiet. There were several other families around but none seemed very loud. We also had a very good meal here.
Overall, I would say we saw a fair amount of children in most restaurants but they all were decently behaved. Maybe we just lucked out. I have 3 nephews so I do know what loud and obnoxious looks like!

We just didn't really see it in the restaurants. I don't know if that had to do with the times we ate, the places we chose, or even the time of year...? Hope this helped and good luck!