A good question.. and I dont know if this is a good answer but I shall try ?
I did both... but I gave up first in my sitch.. I just said enough was enough ? for ME ? Then when it came to the kids and my xw's interactions.. or lack thereof.. I detached.
Giving up = I am done thinking of this person as my spouse and it was time to move on and be Tom ?
Detachment= Letting my xw do her thing.. whatever it was.. and not being concerned about it. The emotional entanglement disappeared.
There seemed to be a fine line for me.. I hope that helps ?