Devil's advocate questions here:
Given the myriad distractions that children provide and the amount of attention that's required to prevent them from swallowing things inappropriately, how on earth do you parents expect to do immersive role play? Do you just roll dice and keep an eye on the kiddies? Do you expect everyone in your group to give up immersive role play to accommodate your desire to not pay for baby sitting? And do you expect them to never feel the slightest bit of resentment about it?
It hasn't been an issue so far. We've suffered through playing in a crowded youth center with ping-pong balls and the occational pool ball flying by and fifty people screaming in the background, in the all-too-frequent cellphone calls by another player's significant other, the occational pause to find the right music for the mood, to answer to door to get food and/or travel to get food, late players, people leaving early to elsewhere/to work/home, pets at other players homes wanting attention/to be fed/to be walked, and so on.
There are times when you can do in-depth immersive RP, and there are times when it is elusive. But that will happen regardless of whether or not children are part of the occation; players are quite capable of derailing a thrilling scene with 20 minutes of Monty Python quotes or bogging down on looking up a rule.
I don't look on other people's children as an impediment to my RP (and they have felt the same, at least those we play with) any more than I look upon the player who drank 3 two liter cokes in half an hour and has to go to the bathroom every 2 minutes, or has to check in with the spouse/SO/etc every so often, or gets easily distracted playing with their dice, or whatever.