1) You cannot have a sweet lips in a 60 gallon tank. They need 200+ gallons.
2) You cannot have a tang, any tang in a 60 gallon tank. They need 100+ gallons.
3) Powder Browns, Blues etc. need 125 gallons minimum
4) Sailfin Tangs need 125 gallons minimum
5) Always QT your fish BEFORE putting them in the tank for 4-6 weeks, either with hyposalinity treatment or cupramaine. Prazi pro for 2 extra weeks isn't a bad idea either
6) You should wait at least 1-2 months before putting any fish into a new tank and add one fish a month after the 2 initial months
7) Corals should not be added until at least 3 months and 6 is much better
8) Quit listening to your wife on the fish tank part, if she isn't doing any research he advice is only going to kill your fish and corals, and waste 100's of dollars maybe even thousands.
9) Don't ever go back to the LFS you went to that sold you those fish and tangs for a 60 gallon tank that is only 2 weeks old on top of that. Only go back to get a refund for the fish after explaining what horrible advice they gave you. LFS are only out to make a dollar the easiest way. They do not care about your fish, if it dies good for them because if you bought 3 tangs for a 60g tank in the first place without knowing the tank was too small or mature, they know you will be right back the next wanting more. $$$ for them
10) Buy several books on this hobby and read read read before you do anything else to your tank.
11) Only do water changes right now, and do not add any supplements. Your tank is going to go through a lot of changes in the next 6-12 months. You need to get a feel for it's requirements before throwing stuff at it.
12) Please take every one's advice on this forum within common sense, but don't go out and do something that one person told you 5 minutes after they post their advice. Wait several days and see what the general consensus is among more elder knowledgeable reef keepers.
13) I wish you the best of luck, and please for this hobby's sake take it very slow and easy. There are a lot of people in the world right now attacking our hobby saying that our fish are destined to die by our hands because we do not know what we are doing. In most cases that is far from the truth, but sometimes it is the truth. Like I said before, read, read, read until your eyes are sore, and then read a lot more. While my tank cycled for 2 months I went to Barnes and Noble everyday for hours and read every saltwater aquarium, invert, fish and maintenance book I could find. They don't mind if you read their books in the store so take advantage of that.
I hope I didn't sound harsh, although I probably did, but people that know, in life sometimes you need to be jerked up by your belt loops and whacked up-side the head sometimes to wake up and listen, and take the best advice that is given to you and easily accessible.