If I were to part ways with Serena, where would she be so I could find her again?

Fort Dawnguard if you sided with them.

Save prior to that though and test it out a bit. I've seen other posts where someone did this and couldn't get follower dialogue from her again.

Always good to save.

Yeah that happened to me :/

And me...and it also happens on the 'wait' command dialogue.

The the Castle if you're a Vampire.

And me.... I eventually went back to my last save, immediately after completing the MQ as a Dawnguard. (At the time I was able to keep two followers btw, which seems to be the case if you've had one when starting DG.)

I had originally sent her to be cured right away. When I reloaded, I kept her as a vamp, and she was ok to wait and dismiss.... I finally cured her again, and she is still ok to wait and dismiss, but I lost the two follower benefit - drat!

Moral of the story - if you have an old save, you may be able to eliminate the glitch...

I suggest keeping her unless she has become an extreme annoyance to you. There is a glitch where she will not follow after dismissing, or telling her to wait.