Maybe, maybe not. Since asthma attacks occur for many reasons (or without reason), a person may get symptoms even if he doesn't breathe in second hand cigarette smoke. On the other hand, some asthmatics aren't bothered much by second hand smoke. If the air is cleaned (with a hepa filter) indoors, anyone will be better off. Barbeque smoke, fire place smoke, marshmallow-roasting campfires, etc... Can cause symptoms.
???? Anything can trigger an asthma attack. The strong odor from the fumes of the smoke on your mothers close could cause the asthma to flare. Best to simply avoid any possibility of exposure to smoke. And get your mom to speak with a doctor about quitting smoking, too.