It was an ice cream cone that brought Joseph Allen from New Jersey to the middle of the Brooklyn Bridge on Monday morning, where he was singing a song denouncing violence as he marched with hundreds of other parents and children to demand stricter gun control laws. Mr. Allen mounted the bridge for the march, along with a group of about 200 people, by some estimates, drawn together by a social media campaign begun by Shannon Watts, a mother from Zionsville, Ind., who founded One Million Moms for Gun Control after shootings at a Connecticut school.