Never.
Bar spots are for people being waited on by the bartender. And the bartender can't earn a living without paying customers. He won't make much off of a mom and 2 boys who can't drink alcohol.
Besides, I tend to think of bar seats as being for individuals or maybe 2 people who are having a drink while waiting for a table to clear.
Not to mention that it just seems highly inappropriate all around.
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We sit "in the bar" frequently, as a family. In some restaurants it is the only place they have the sports on the TV. But we sit at a bar table, not AT the BAR. IF there is a person in the bar area who is going to be a little far gone and nearing belligerent, they will be seated AT the bar, guaranteed, not at a bar table. When you sit at the bar, you are essentially inviting conversation. When you are at a table, it is more private.
And there are TONS of bar/restaurants. Outback, Longhorn, Ruby Tuesday's, Houlihan's, Wee Pub, and so on... and all of them have tables in their bar, AND a BAR. The folks sitting at the bar in those places are usually there for a long time (an entire sporting event, multiple drinks long), or in less corporate type places, they are hanging out with their date until a table comes available.
After 9:00 pm on a Saturday night is not a place for kiddos period. Couldn't get a sitter? Then stay home.