thousandqords.....remember that the kids will take their cues from you. They will observe your moods and body language and many other behavioral clues that we radiate.
I would suggest that you take special care to make the move be a pleasant on for them...as much as is humanly possible...lol.....
You are the Captain of their ship...for the day to day things that kids take their security feelings from.
If the Captain is calm, confident and pleasant....then they will pick up on that.
things like...ordering pizza and watching movies together...or you reading them stories from book each night, while having hot chocolate...and going for nature walks together, and playing board games together.....Having music on, in the background, all of the time....Having the best thing/worst thing at dinner, around the table, while eating. (what was the worst thing in your day...and, the best thing).....
I think the kids will instinctively know why you will be moving....I suspect that you son was just seeking validation that what he thinks is true.....