You've received a ton of advice, guidance, tips, and helpful information here.
My suggestion is to step back from this for a while. I would want to confer with the L and really tell her/him what you just said to us here. Ask for legal advice from the L and it also wouldn't hurt to seek a child psychologist for input as well.
For now, I would not respond to W's email. You need to gather some more information before you make any concrete decisions. A few more days would not hurt at all.
I get that you don't want to miss this great opportunity to chart a new life for yourself and S12. My mother moved several states away when we all were very young and we weren't 'damaged' as we were allowed to visit our relatives and father. Yeah, we all dealt with it when the move took place. This isn't the first nor the last time that a divorced parent moved several hours or states away with the child/children.
The MAIN thing is that the children be allowed to have a R with the other parent through phone calls, letters/cards, and holidays/trips.