I've replaced grout in my shower before - it's a really messy job. You have to remove the old grout - clean the dust out really well, make sure it dries completely and then put in new grout - make sure you do it so there isn't a grout film on the tiles (or you have to acid wash) - it wasn't fun.

If you just want to change the grout color, go to Home Depot and get a colored sealer/stain and paint it onto the grout (carefully). It will penetrate into the grout staining/coloring the top portion of the grout. I did this on a bathroom floor. I never put bleach on it - so I don't know if the clorine in the pool water will affect it. I would be more concerned about sun bleaching - but if it did you could color it again (they even have white, if you decide the colors won't work).