I did exactly this a couple of years ago - separated from my partner of over a decade, sold the house we shared, and left the expensive South East taking the kids with me, buying a cheaper house in my home town.
Understandably, the ex wanted to stay in touch with the kids, so after a time in temporary accommodation while he got his situation sorted, he eventually also moved out of the area, found himself a new job in the same town we now live in, and sees the kids regularly.
It was horrible at the time, but there was no way we could have afforded to run two separate households in the area we lived.
The kids were naturally upset to be leaving their friends and familiar lives behind, but the situation at home 2 years on is now much happier and calmer, it wasn't doing them any good living in such a hostile environment before the separation. They have settled well, found new opportunities, and still remain in touch with their old friends, so have the best of both worlds.
It's not gonna be easy for your kids, but it isn't the actual separation that causes them the most hurt, it's the circumstances that lead to it being necessary....so if you've already made the decision to go your separate ways, get the ball rolling so that they can settle into the new status quo as soon as possible.
I now have my family close by - something that has helped immensely being a single parent in what was, to begin with, a raw and delicate emotional state. I also have less financial pressure due to living in a much cheaper area (i.e. much smaller mortgage) which is a huge help when adjusting to living on one salary instead of two.
By far the best move I have ever made in my life....and yet I agonised over it for months before finally taking the plunge.
Only you will know if the same decision is right in your situation - but follow your instinct, it is usually right. Don't let anyone make you feel that you ought to stay where you are if everything inside you is screaming otherwise.