Simplistic as it sounds, it depends on the child. I have two sons. My older son was traumatized for several months when we moved to California from Pennsylvania. He was 18 months old when we moved. My other son was moved from Ohio to Florida in his first year of high school. He had no problems at all.
Every kid is different. I’d look at how each of your children adjusts to changes in their environment or routine, even those of a very small nature. Past experiences are the best predictors of future behavior.
Unless your children are emotionally fragile (and by that I mean “diagnosable”) in some way, I’d move to a district that you believe would be better for them, socially and academically, in the long run. And there’s no question that having a parent at home in the evening who isn’t tired out from a long commute (or, worse yet, still stuck in traffic) will be much more beneficial for them.
If you haven’t done so yet, I’d recommend that you speak with several of their teachers and counselors at their current school(s) to see if there are any issues that might prove problematic if you make the change you are considering. The other thing I’d suggest is, where possible, to make the kids part of the decision-making process. Being a kid can be scary: kids can start to act out when they feel like they have no control over what happens in their lives. Keep in mind that I am not advising you to ask your children for their permission to move. Believing that you are the adult and parent, I am of the strong opinion that this is YOUR decision to make. But perhaps you can include your children in the choice of a house, when you’ve narrowed it down to 2 or 3. Or let them research extracurricular activities in the new neighborhood, and choose one or two in which to participate.
Whatever it is, don’t discuss the pros and cons of moving with them, or involve them in conversations about which school district would be best, etc. These are adult decisions, and having them hanging above them will only create anxiety in their minds. Kids have much more difficulty dealing with uncertainties in their lives than they do with changes stemming from decisions made by parents who clearly demonstrate their love and support for them. It seems evident to me, by the questions you raise in your post, that you’re in that category of parent. Good luck!
