When parents get divorced, they spend a lot of time thinking about what is best for the children -- or, at least, what they think is best. While it's good to put the children first, do not forget that they have opinions and desires of their own. It's wise to talk to them and find out how you can make things go as smoothly as possible for them.
For instance, many children wish they could tell their parents how much they love both of them. This can become a point of contention when the parents are not on good terms and want to talk down about each other to the kids. Children don't enjoy this since they love both people equally.
Children also often feel like it's unfair to them to track the exact amounts of time they spend with each parent. This makes sense from a child custody perspective -- you need to share time with the kids in accordance with the custody arrangement -- but this does put pressure on the kids. They may feel like they always have to leave when they're having fun.
By the same token, though, children do not want their parents to work to keep them all to themselves. With some exceptions, most children want time with both of their parents. If mom or dad makes that impossible, they can resent it -- perhaps for the rest of their lives.
As you can see, you have to deal with children delicately during a divorce. Make sure you understand what legal steps you should take and how to make the right decisions for their well-being.