[lcstorc]

Welcome to RS!
There are several popular ways to get rid of Aiptasia. One of the most common is to get peppermint shrimp who like to eat it. Be sure to be true peppermints and not the camel shrimp that are often sold as peppermints. Do a search to see pictures of both so you know the difference.
The next most popular way is with a product called Joe's Juice. It comes with a syringe and you just put a small amount in the mouth of the anemone. I just did this about 5 minutes ago amusingly enough.
I have also heard of people using kalc paste, lemon juice, and boiling water but I have never tried these methods.
As far as the tang and the copperband the best thing you can do is try to reduce the tangs home territory (or what it recognizes anyway) You can try rearranging the rockwork and see if that works. Or you could temporarily move the tang to a qt tank or even a fuge or sump for a couple of weeks. Then it will be the new fish in the tank and less likely to be a bully. It may get agressive again but that is about all you can do short of getting rid of one of the fish.

HTH.