Lots of people with kids. Not stuffy. I would not take a two year old though as the meal itself is expensive and lengthy (easily one and a half hours - more likely two) - and I, myself (you can make your own decision) would not want to risk getting halfway through a $100 a person meal and having to finish it out of a styrofoam container because of meltdown. But a six year old can sit for two hours.
ETA: Kids are different. Both mine would NOT have made pleasant signature dining companions as toddlers, both have been capable of doing it since about five or six. We went with friends who had a seven and eight year old and ate at Flying Fish, it pains me to say it about friends, but neither the kids nor their mother were pleasant signature dining companions - we should have stuck to Spoodles.