My opinion is that kids at Trader Sam's are fine - I've seen it on nearly every visit. Its so loud in there, kids would not be a bother to adults enjoying a drink. I would probably not take bar seats up with kids, but there are tables where I think its fine.
The problem with OP's plan is that there is a good chance there is a wait to get in that time of day. And even if you can get in relatively quickly, that does not guarantee you a seat - especially a table large enough for a party greater than two. The place is very small and there is standing room which they allow. Every time we have gone, we've arrived 30-45 minutes prior to opening and have been able to get a seat. After an hour or so, we leave and there are people stalking our table inside, and others loitering outside with pagers waiting to get called in. I believe Trader Sam's opens at 3pm now, so early evening would be primetime IMO.
I'll also add that the Trader Sam's menu is relatively small, appetizers, and many of them are unique and may not appeal to younger kids - unless they have advanced palettes!