But recently she has started mentioning divorce even while she is in a good mood. Just things like, "We still have to have a serious conversation about ..." To which I don't respond, other than slowly nodding.
I wonder if she is actually saying that to get a reaction from you. Seems like you're not giving her anything but a nod, which could be confusing to her. Like do you want a divorce or not? Are you agreeing or disagreeing when you nod?
If you DON'T want a divorce, what about saying something like... "I've heard you say you want a divorce. I don't want one. I'm happy to talk about it more if you'd like".