The W-2 should list all the states which are subject to tax withholding. Although it is not unusual for an employer do only do the works state, since the residence state gives a credit (essentially the residence state is not "subject" to withholding).
Either way, you should go with the current one. It's gonna be a lot less work for everyone. You don't need s corrected W-2. You can "make one up" at the W-2 screen in TT.
As you said, your case is special (the onerous NY rule on telecommuters).
