Bryopsis is an algae you DO NOT want to deal with, as John mentions. It's a notorious nuisance algae.
You're on the west coast, so actually, caulerpa is illegal. Of course, it's everywhere, but there are good reasons for it to be banned here. The concerns are that if it ever saw our natural coasts (as in: It was unnaturally introduced by a hobbyist who didn't dispose of it correctly), it would thrive, and choke out a lot of the natural life that's there. To dispose of it correctly, place it in a plastic bag and freeze it for at least 24 hours. The freezing breaks down the proteins that hold the plant together, effectively killing it. Then, dispose of it in a place where it doesn't have a chance of making it to the ocean.
The reference to caulerpa being toxic was a little misleading. Caulerpa can go "sexual," releasing its spores through your system. The first problem is that if the sporing event is large enough, it can kill fish/corals/etc. in a "toxic" manner by choking out their access to clean water to breathe. The second problem is the spores will land all over your tank, including your pristine display, and you'll have a huge caulerpa farm. The only way you'll ever get rid of it at that point would be to start over with new rock. But I'd bet your nitrates will be low.
Some people control the sexualization by running their refugium lighting 24/7, to "trick" the caulerpa into confusion. It might work, I'm not sure, but it reminds me of freezing nitro-glycerine so it doesn't explode. You're just asking for trouble.
Chaetomorph, on the other hand, is extremely easy to control. It should also be extremely easy to get a hold of, just about every reefer has some. It's just the responsible and simple way to utilize a macro algae.
