I want to move 15 hours away from my children
Does your wife and kids want you to move so far away?
No, she wants me to move closer to her
If you are no longer living with your wife, and if you have a pressing reason to move away, then it is okay to take care of that need. However, you should still be there for your kids, even if you don't have full custody, and your wife will want you to be close enough to be a part of their lives.
I will start paying for them to visit me and try to find a girlfriend to replace my wife.
If you are now fully separated, it is up to you to date whomever you want now! But I believe you still need to hold responsibility for your children, as they are a part of you and want to be in your life. You can only watch them grow up once!