It is telling that the majority of this thread is about how single or childless gamers should accommodate couples with children and not about how parents who want to game should accommodate players without children.
I think is a byproduct of who is likely to be reading and posting in this thread - gamers with kids and gamers whose group includes parents. If you have any advice for the parenting group I'm sure they'd be willing to discuss your point of view as well.
Here are a couple of "rules" I would advise for parents as examples. Keep in mind, I am a single person without kids of my own whose current group includes 4 couples, 2 of which who have young children, so some of this is from my personal experience and some is from what the parents have told me about other unmarried non-parents they've played with in the past.
1. Don't apologize for your kids acting like kids. Sure, if the kids are acting particularly troublesome one session an apologize is okay. In general though, apologizing because your children is asking for something or needs some quick attention is unnecessary. If basic parenting bothered me, I can discuss alternative arrangements with you personally or find another group to game with. (I realize that can read as snarky but that's not the intent in which I mean it to come off, I just can't think of better phrasing at this time.)
2. Make allowances for the fact those who do not have kids are not parents and sometimes make mistakes when interacting with your children. For instance, we can forget that kids tend to put small objects in their mouths when they show interest in our dice or miniatures. We don't also know the snack rules or we sometimes to forget to ask permission if your child asks us for some snacks. If we see your child about to do something dangerous or troublesome we may spontaneously yell out "Hey!" or "(Interest child's name here)!" to get both their attention and your attention.
3. Unless you
really want our uninformed opinion on parenting or how we think we'll behave as parents, please don't ask us. We're approaching the topic from a distance when anything we may say is undoubtedly of personal significance to you. For instance, any conversation we have about how we would discipline our children is speculative for us whereas you are having to make real, concrete decisions with immediate actions and consequences on the same topic.
4. Finally, don't be afraid to have a limited conversation regarding parenting with the other parents in the group during downtime. We won't feel alienated as we often talk to certain members of the group about interests, work, people, etc. that are not shared by everyone. Both parents and non-parents should remember to keep these types of conversations limited though.
All that said, I really enjoy having the kids around in our current group as they exude an infectious energy that is currently lacking in the other areas of my life right now.