Horrible news, I’m so sorry for you both. Like others here we’ve been through this a number of times and there’s no two ways about it, it’s just a terrible thing to go through. You’ll be feeling pretty helpless as you see the pain your wife is in but you’re helping her more than you know by just being there. That said, don’t play the rock at the expense of your own feelings, give yourself some time (and space if you need it) to grieve and it’s OK to be angry at the unfairness of it all.
There is plenty of support available but my wife and I actually retreated into ourselves (as a couple) and helped each other through it. Might not work for everyone but in a weird way it made us stronger in the long term.
Finally, the worst will pass. When it does, it isn’t a betrayal to start thinking about the future again. You won’t forget your twins, they’ll always be a part of you now, but that doesn’t have to be the end of your story.