Mostly they do not get a choice. They are sent on deployment and that is that. Iraq was a "you are going" deployment. That is what they sign up to do if needed.
This trip of my son's was a hands up to go one. He was there as part of a media unit.
His wife negotiated with him.
If he went for the 2 months then she would get to go to New York for a week (no kids) to see her great friend who has married and moved there.
This will happen in March and my son has leave to be a house hubby with the 4 kids.
Luckily he is just as good a parent as she is with the kids and the housework.