When mothers remarry they usually get the largest amount of custody with kids. So the children easily like mom better, because they are with her more. So dad has to try to make the short time he has with them more fun and appealing. Also the new stepfather has to try and make kids who have never met him like him. In both of these fathers situations they usually turn into what is known as "Disney Land Dad". This involves excessive gift giving, relaxation of rules, and lack of discipline.
Parents, even divided ones, should never try and pit children against another parent, or try and fight for affection. parents need to join in in co-parenting. They need to support each others parenting. It may seem hard at first, but it will be worth it when you know that the child is always getting even, and equal parenting from each parent.