Depends on the age of the child. Second hand smoke exposure in large amounts or constant exposure can cause asthmatic issues.
Just anecdotally, would you say the prevalence of asthma, breathing difficulties and allergies in general have decreased since cigarette smoking became far less prevalent, stayed about the same, or increased since then?
I'm certainly not advocating smoking, but I ask because my own recollection as a child during the late '60's through the '70's is that there were very few kids with asthma and allergies in general, despite cigarette smoking being quite common.