Where have the kids lived/stayed when she has moved out? Have they gone with her, stayed with you, or split time between you and her?
If they've stayed with you, meaning she voluntarily left them with you, that should be a major factor in your favor should it ever come down to a custody dispute.
I agree, your parenting history versus hers will mean something, though we've learned court can too often be utterly clueless and stuck on default preferences and default policies so don't be too confident court will pay attention to the historical facts..
She says she is not moving out until forced to (I assume when divorce is finalized). My attorney told me absolutely do not move out or start dating. Her behavior is baffling and even after all these years still cuts me to the core.
I totally agree with your attorney. If you moved out it would be too easy for her to "keep the kids in the only home they've ever known, after all, their dad left them". While the court could potentially order dad to be the one to move out, but her historical
pattern of moving out to live with other guys should be enough to reduce that risk.
Let me expound on an admittedly generalized scenario. Most often men are the ones to be will to wander away from the kids and start another relationship elsewhere. On the other hand, women are most likely to cling to their kids, almost as an extension of themselves to control and sometimes even parentify. (Most cases members describe here are of that sort.)
Yet there are exceptions to possessive mothers, and yours sounds like she may be one, where the spouse/mother wanders away and places more attention on the new adult relationship than parenting the children. Is that the case here?
Last thought... Historically, the most common and acceptable reason to end a marriage is infidelity. You did not have to accept her back into your marriage, not even once. You may have perceived it as the least bad option for you, but you can now look back and wonder how you ever let her leave and return so many times. That's the past, nothing to change there, but you can change your future. Look forward.