Depends on what state you live in. I live in a no fault state, so there is nothing I can do to stop it, even if I don't sign. In other states, it takes much longer and some things, such as infidelity matter when it goes to court. Some states order marriage counselling. In most, if not all cases though, you cannot stop it from happening.
The process will take several months at least and an attorney can delay it as well. Take heart, in my sitch, my wife was full speed ahead for a D. Filed in June, first court date in July which temp. custody orders were set. Then went to parenting class.
The only thing we disagree on is the split of the kids and she can end this. I even told her I'd compromise a little with that. It's now December and I've heard nothing further so as far as I know, we're still married. I'm going to call the courthouse just to doublecheck the status this month.
My point is, my W was spewing threats and had moved very quickly in the beginning, now things have slowed way down in that regard. There's hope, and I think you're handling things as best as can be expected.
Puppy, Coach, Greek and Gnosis are good conselors. I also like Robx, Gucci and Steve McQueen's perspectives as well.