So, here's the thing with kids, especially queer kids.

Generally, being awkward in this situation isn't something that comes naturally. They are taught the awkwardness.

And what you need to demonstrate to them is that you're allowed to be imperfect, and make mistakes with words and terms, and language, but that the mistakes are just habits, and that once you strip the habits away, you see each other for who they are. The habits will sort themselves out after that.

Not sure of their ages, but they sound like the kind of kids that would be accepting of the situation. I would treat it like its totally normal while also acknowledging the societal challenges, and making sure to hear their perspective and experience with it

It doesn't sound like your kids will have much of a problem, but there's always an adjustment period with any transition. As long as everything is explained clearly and openly, and they are given some space to adjust, it'll probably be fine.

EDIT: One thing, you and your wife don't need to bombard them with details about her transition, unless they explicitly want to know something. In my experience, too much too fast can make the adjustment harder.