One thing we have seen time and time again when observing divorcing couples is that often while parents bicker and litigate about what the “best interests of the child” are, they don't actually pay much attention to what is important (and not important) to the kids themselves.
When you take a picture of a toddler, do you tell him, “Go over there. Stand still! Head up! Look this way! Smile!” and then take it from a standing position, where the camera is about 5 feet above the ground? Or… do you watch him as he's playing on the playground and catch him at that moment he's gleefully burying his feet in the sandbox, squat down to be his height, and capture the moment as he's experiencing it? There's a big difference there, right?
Children of different ages (exacerbated with different temperaments, backgrounds, etc.) are at very different developmental stages. To assume that a singular thing is important or not important to “children” as if they are all one singular clump, completely misses the mark. Similarly, when divorcing parents (especially those who have been the children of divorced parents themselves or have had experience with divorce up close) try to impose their own values about what divorce “means” to “kids,” what they are often really doing is just trying to use the kids to elevate the status of their own beliefs about how things “should” be.
It is important that parents set aside our preconceived notions about what divorce means to children … our children … what is important to them, and what is not important to them. For example, imagine this: You start a conversation with your daughter by saying,
“You know that Mommy and Daddy are no longer together. Mommy has started seeing someone new. His name is Sam and he is coming over for dinner tonight to meet you.”
Your daughter starts whining and looking upset. At this point you launch into a monologue about how much you love her and how this doesn't mean Sam is going to replace Daddy and how the divorce wasn't her fault, etc. etc. Meanwhile, what's really going on in her head is the cartoon she just saw about a robot factory where evil robots that look just like humans are made, and so when you said that you were “seeing someone new” she was worried about the fact that you're inviting an evil robot over to dinner! Or maybe the name Sam conjured images of the Uncle Sam poster with a white-haired, pointed-finger, stern-faced man. Her reaction may have nothing at all to do with divorce, or Daddy, or anything else in that universe.
The preferences and whims of kids (especially young children) should not be what dictates how parenting time should be apportioned, how much child support should be paid, or any of the other provisions of the custody arrangement. However, that doesn't mean that their perspectives, input, and thoughts should be wholly disregarded either.
Some parents find it useful to work with a counselor or pediatric psychologist to try to elicit this information. Others are able to ascertain it without the help of a professional. The danger of going it on your own is that even if you don't do so intentionally, it's easy and natural to ask loaded questions or to unwittingly make suggestions about what the “right” answer is, in ways that dealing with someone more objective doesn't happen as much.
One thing that is hard for many divorcing couples to grasp is that very often the children really simply do not care about the status of your relationship with each other, unto itself. They don't care if you love each other, hate each other, can “be friends,” can't be, etc. What they care about is the effects of that on them. They don't like to hear parents yelling or arguing at each other, because that is scary and makes them feel vulnerable.
Similarly, some kids of divorced parents might express that they are “really annoyed with divorce.” But it may have little to do with what you think “divorce” is. It could be they dislike the logistics always having to remember which house their school backpack is in, or their favorite pair of shoes, or where they left their umbrella.
On the other hand, it goes both ways. Some kids of divorced parents are actually really happy about the idea that they get two birthday parties, two Christmas trees (or one Christmas tree and one menorah, or whatever), two (different kinds of) of family vacations, etc.
If the life change were that you were moving to a different city rather than going through a divorce, you might understand that your child is thinking about things like leaving their friends behind, having to be the “new kid” in class, orienting toward a new school, and otherwise leaving behind familiar things for a new world of many unknowns. You'd likely adopt an understanding posture and would suggest ways to keep in touch with friends. You might offer to let your child pick her own color of paint for her new room. You might emphasize all the amazing aspects of the new school, and how you'll be so much closer to grandma, and that here they can join the swim team because there's actually a pool nearby.
To the extent possible try to adopt the same kind of demeanor as you think and work through your child custody arrangement. Acknowledge their feelings when they express aspects of the change (the divorce) that they don't like. Encourage them to look for positives out of it. Address the aspects of it that they mention or indicate is important. Avoid forcing your own views or pain or feelings or assessments or values or preconceptions on them. Doing this will be the best gift you can give your children – and possibly yourself as well.