While you feel there are three options, there are really an infinite number of options, so keep an open mind as your life and this situation unfolds.
I don't agree with your friend. Your children should see you AS OFTEN AS POSSIBLE. So that means, you move as close as possible, hands down. DO WHATEVER IT TAKES, it's not rocket science.
My ex did not do this, in fact he moved away in his pain. (I was already divorced when I came to this board, I came 2 relationships later.). So, I raised my children basically without their dad in their life. He bitterly regrets it. They wish their dad cared enough to be involved. It wasn't that he didn't care, he was just in too much pain, and probably got bad advice from friends/family. I do know his parents initially encouraged him to move their and convinced him to fight for custody, with the delusion that he could win and raise them there. Of course, that wouldn't work.
The problem is...it can't be undone. They are now grown.
You have a chance to to at least fix the father-child situation. And possibly the situation with your wife.
Selling your house will make this worse. Go move back there. Find all kinds of jobs until you make a great job work in that situation.
THEN work on your relationship with your wife.
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For your relationship with your wife....what were you two doing when you fell in love? What were you doing when things were great between the two of you.
All the BEST.
sg Love is PATIENT, love is KIND, LOVE never fails / DB since 2001