Can smoking around children influence them to smoke?

Yes. Yes, of course. Children look up to their parents/adults for guidance and direction. In addition, second hand smoke promotes health problems in children including asthma, ear infections, etc. There are many reasons to quit smoking, but the presence of a child is a very strong one. Best wishes and good luck quitting!
Sure it can! Children model the behaviors of their parents. (ever caught yourself sounding like one of yours?) if they see you smoking, they may associate it with being grown up, and smoke to gain the same association in themselves. They may grow accustomed to it, even addicted to it, through you. If you love your children and care about their future, quit smoking!