Unfortunately, you’re often not dealing with smokers, you’re dealing with assholes who happen to smoke. The non-asshole smokers would not be smoking in a non-smoking location.
If the area is posted non-smoking and they’re smoking anyway, the best you might do is politely point out the sign. I have been in places before that I simply didn’t see the sign, even when it should have been obvious. They’ll either do what I would, which is apologize and quit smoking or move elsewhere - or they’ll be an asshole.
If the area is not posted and is outdoors, and you ask me POLITELY to not smoke around your child, I will probably move elsewhere with much internal eye-rolling. I would do it because I’m nice like that, but you’re much more likely to get a bad reaction in that situation. Also, if you’re asking me for a favor, you should be extremely polite, even apologetic perhaps. Getting huffy or self-righteous or any of the other nonsense I’ve been subjected to by fanatical nonsmokers ain’t gonna help your case any.
I understand not wanting your kids to be bathed in cigarette smoke but, as someone already mentioned, I’m not buying that the trickle of smoke from my cigarette is causing problems that the exhaust cloud from that diesel that just drove by ain’t. Not to mention, it’s a big wide world outside. Unless I’m standing over her blowing smoke in her nose, it’s unlikely she’s being exposed to cigarette smoke.
I will grant that I am more sensitive to these things than a lot of smokers - I do watch where my smoke is going, and move down- or cross-wind to avoid smoking people out. But most of the people I know who smoke would react well to a polite request to move away a bit. I can’t help you with the assholes.
Things not to do: go into ridiculous coughing fits; wave your arms around while complaining loudly about the cigarette smoke; act all offended and huffy and holier-than-thou. If you’re acting like a jerk, you’ll probably get the response you deserve. (Not saying that you would, that’s a general “you”.)
I also bitch out smokers for leaving butts everywhere. That’s just nasty!