I have just asked people if they would please move away from us while smoking because we have allergies and asthma.
Occasionally, I would get dirty or puzzled looks, but the people usually complied. When they haven't, I have just moved because our health is not worth the risk that comes with second-hand smoke.
When my baby was 8 weeks old, I was breastfeeding him in a lady's lounge at a reception site when a woman came in and started smoking---even though it was a non-smoking site and the weather was perfectly fine for her to go outside and smoke. I asked if she would please stop because I had an 8 week old with me, and she just started raving at me as if I had asked her to chop off her head. I told her that everyone should know NOT to smoke around an infant and that it was a smoke-free venue, but I knew what I was dealing with, knew that continued conversation with a nut wasn't going to do any good, and just left and found another place to feed him.
In a park situation, I would hope that the other adults would compy and be understanding. If not, you know what kind of people you are dealing with----people who feel that rules don't apply to them and who don't care about anyone or anything other than themselves and their own desires.
There is absolutely NO reason to be smoking at a park where children are playing. NONE. However, there will always be those people. We parents have every right to ask them to stop, and we should not let their possible negative responses keep us from asking.
Most of the time, most smokers are sensible, understanding people who get it and will move. In those cases where the opposite is true, it is best to move yourself and your child away from the smoke.
Good luck and never be afraid to ask for what is best for your children and you!
J. F.
ETA: To the responder above me trying to equate car fumes and dairy smells smokers' smell, who said "most westerners smell of sour milk....." REALLY???? I live in the west (NV).....we actually have a dairy farm here in Las Vegas, probably 25 miles from my house, which I have visited ONCE, hardly enough to make me acclimated to the smell. Not one of the employees there smelled upon entering the facility----which is when it would have been easiest to detect. I also have people in NM who have dairy farms all around them. When I visit them, or they visit me (away from dairy farms), they have no "sour milk" smell. In addition, I can't think of one person who is never around car fumes, so by your reasoning, we are all around car fumes and must all smell, but not notice it. So, how would that be offending anyone? Yours is a 'patently ridiculous' comparison.