Being parents, we try to make sure that our kids are OUR problem, not someone else's. We expect the same sort of courtesy from other parents.
My campaign is full. Way full. Waiting list full. When everyone makes it, there's 11 players, 1 DM (yours truly), and an occasionally wandering to-and-fro black cat. I do have a hard and fast "seen but not heard" rule. You want to bring your kid? Fine. Let me know ahead of time so I can be mentally ready. Keep them quiet. You want to bring an S.O. to watch? Fine. He or she should not try to contribute something to the in-character game flow.
Prior experiences have made me have to crack down like that. Otherwise I get walked all over. Worst (and most recent) incident:
A few years ago, I ran a Kalamar D&D campaign. I have this former friend of mine, we go way back. He and his wife have 3 kids, and adopted 4 more. When we were starting up the campaign, he asked if he could play...and bring three of his sons, ages 18, 14, 11, if I recall correctly. I know I have the first two ages down pretty accurately. I almost want to say he brought along a fourth, but I honestly can't remember. It was at least 3 kids. Maybe 4. Since we were such old friends and he was one of my ardent veterans, I reluctantly agreed.
Well, the 18 year old was excellent (great kid all around)...the 14 year old kinda okay, the 11 year old was a freaking nightmare. And I was the one stuck doing Kid Control while, across the room, he was chatting up one of my female players. Yes, the guy's married. :\
They only came for one or two sessions. I implemented the abovementioned rules, and that's how it stands.