Yes, people live on St. John and commute to STT for work (and some do the opposite). Some do it because they have no choice, others do it voluntarily. As is the case with "commuting" just about anywhere some people will tell you they don't mind it, others will tell you they hate it. How it will affect you or your wife is something you have to figure out for yourselves.
In addition to the ferry travel time (about 20 minutes between Red Hook & Cruz Bay and 40 minutes between Charlotte Amalie and Cruz Bay) you have to factor in "waiting time" at the ferry dock and travel time between your home and the ferry dock and from the ferry dock to your place of business. Also, you have to consider the logistics of getting to/from the ferry dock and your home/place of business.
Now, if your wife has to be at work by 8AM and won't leave her job until 8PM that means she's pretty much locked into taking the ferry between Red Hook and Cruz Bay and will have no choice but to leave Cruz Bay on the 7AM ferry and catch the 9PM ferry for her return. Adding in travel time to/from the ferry dock and you'll see she's in for a VERY LONG day. She may find that acceptable but then again she may say "No Way".
Most people making the move to the Caribbean cite a desire for a "simpler lifestyle" as one of their main reasons for relocating. If that's you, then you should serious consider the impact commuting between islands will have on you achieving that goal.
I don't know where you live and what type of commute you or your wife has now but I can tell you from experience that you'll be much happier opting for the shortest and easier commute possible. For 20 years I used to live in the suburbs of a major city and had a minimum 90 minute commute (sometimes stretching to 2 hours) each way. It got "old" very, very fast and i grew to hate it. I then changed jobs and relocated to a different city where I had a 12 minute commute (and that was when I got stopped by one traffic light otherwise it was 10 minutes). I became a different person and quickly realized there was not enough money in the world to make me to want to ever again revert to a longer commute.
Don't let palm trees, sandy beaches and turquoise waters cloud your judgement. Take off the rose colored glasses, get all the facts then make an informed decision.