^Of course! Tangaroa Terrace is a standard restaurant. Trader Sam's is a watering hole, but wonderfully themed. Tables are all ages; only the bar is off limits to kids. I've seen plenty in there during the day.
You can indeed bring children with you, but (I think) Trader Sam's turns into a bar after a certain time (9pm? Not positive, I'll have to check) and therefore turns to 21+. I'm going off of what friends with kids have told me as the Disneyland website doesn't make reference to this change on the page.
<3 There are a million cupcakes in the world but only one is Cupcake Terror. <3
Tangora Terrace was ok - I suggest only going if you have time to spare.
Trader Sams can be as bad, I was there while I'd say it was "moderate" busy (which would be light for the average bar), and spent about 10 minutes at the Bar trying to get a Bartender to acknowledge me... instead one was flirting with a blonde, and the others were yacking with each other towards the back of the bar, along with the table server.
I couldn't even get a "We'll be right there... " seriously waved my arms and everything, Wife and I knew what we wanted. We were Hungry so we just went elsewhere dumbfounded at the poor service.