Well, I've got to say that this is amongst the most selfless questions I've received since doing this website.
In a nutshell, I can tell you what my wife tells other women who are considering marrying into ugly custody battles-- take a long hard look at the present, because it will be your future. Having endured it for five years, my wife's advice is that women should avoid men like me and your fiancee. It's taken as much a toll on her as it has on me, and it takes a tremendous commitment to keep a marriage together throughout it all. A stepparent must either be a masochist, or a very rare and special individual, to stick around for his/her spouse and stepchild(ren).
On the other hand, if your fiancee is as wonderful as me, I guess you really have no choice.
It's really up to him to figure out how to manage his stress. For me, it was many things (when I look back):
I think the most that you can do for him is to encourage him to figure out what things will best keep him grounded and sane, in the midst of the insanity and misery, and give him the freedom and support to do those things.
- Weekly counseling with a very experienced family psychiatrist was a private sanctuary for me to unload, try to stay grounded, try to stay positive, and feel validated.
- Reading all about child custody was a way to remove some uncertainty about the situation, which relieved some stress.
- Reading all sorts of introspective literature (i.e., including stuff like M. Scott Peck's books, quickies like "The Four Agreements", and even Biblical stuff like "Book of Job") helped me keep things in perspective and maintain hope.
- Doing fun stuff regularly (whatever that is for you and him) helps to balance life.
- Journeying further into my spiritual roots was timely for me.
- And NOT putting the rest of my life on hold, to the best I could manage everything, likely helped me spend some of my attention and focus on far less depressing and discouraging matters.
Obviously, self-destructive choices aren't reasonable (i.e., drugs or overindulging alcohol).
As you can't really do much for the custody battle part of it, you CAN help him dress his wounds and figure out the best ways to stay healthy and strong. And make room in the schedule and the budget for whatever reasonable outlets he (and you) can identify.
It's a very hard thing to appreciate -- when you're in the middle of it -- but hardship bears many gifts. I'm a stronger, wiser person for it. I'm a better father for it, as I never take a minute with my daughter for granted. When I'm with her, I'm WITH her.
My wife and I are likely closer for having gone through this together. Sure, we hate it all. But we've suffered together. And, as my in-laws have commented-- if we could endure all this during the early years of our marriage, we will be able to endure anything together.
So... your big decision is, are you okay with this as your future? And if so, help your fiancee integrate stress management into his life.