When kids are acting up, such as crying for something one of the worst things you can do is address it right away. It reinforces in them the idea that if they act up they get attention. It reinforces a negative. However after ignoring for a while they continue, you have to address it. It's not easy, you have to walk a thin line.
Agreed. However, you do not allow this to happen in public. Remove them from public and then they can cry all they want while you ignore them.