Now, I am nothing but an amatuer, but my experience with Grape Caulerpa may give you a little insight.
Terrestrial plants generally take their sexual cues from photoperiod. Pot growers know this. When the lighting period gets shorter, the plants enter a reproductive stage, and begin to flower.
I had a lot of problems in my refugium, which was on an opposite photoperiod from my main tank. It would go sexual, die off, then re-appear. When I turned my refugium lighting on to 24/7, The Caulerpa got great growth and has never disappeared or gone sexual.
So keep in mind with the Caulerpas that certain lighting regimens may mess you up. This is from my own experience, but I have heard the same from other reefers on this board.
I am buying plants for my Seahorse tank tomorrow, please feel free to contact with any questions you may have, as I'm about a week ahead of the game than you. I don't know much, but I am trying at this very moment.