That first species is grape caulerpa -- it's a godawful nuisance, and I am currently battling it in one of my tanks - the previous owner thought it was a good idea to have that in the fuge.
They say that once it's in the tank, it will never come out -- it grows quickly, and will grow into/around things (rocks, your favorite corals) , and sends runners into live rock. If you try to get it out, it will break into pieces, and will regrow from those pieces.
Going sexual isn't the big problem with this species -- the main problem I have experienced with it is the fact that it grows so quickly and that you can't get rid of it,.
So my response -- KILL IT WITH FIRE! Seriously -- I would take that rock out of the tank in case any pieces stay behind. It's that much of a pain.
The red one looks pretty cool -- I would keep it.