He says that the building won't allow it. Why shouldn't they? It is a New York coop building so they are strict.
Isn't your super involved in supervising/approving the installation? Usually, if any alternations to the building plumbing are involved (anything on the other side of the wall, which would likely be the case if you are raising anything on this side of the wall (i.e. you have to cut to wall to move the pipe)), you have to involve the building, and they will either allow it (and charge you for the time approving and supervising the changes) or they won't. The co-op association owns everything that isn't in your apartment (well, in a co-op they technically own the apartment, too; I guess it's better to say that they
control everything not in your apartment). So anything that involves having to do something on the other side of the wall is a big, big deal. Anyway, you could talk to your super about what the issue is and what you want your contractor to do, and maybe he can give you some insight to the building's typical position on these things, and what it would cost. I'm guessing a LOT.
I'm surprised that bottle traps are even legal in New York City. It has one of the most conservative plumbing codes in the country. This is for obvious reasons: massive amounts of multi-unit buildings, where doing something hinky in one apartment can ruin the day of people elsewhere in the building, and plumbing practices that don't
usually cause a problem (say, one in a thousand times there is a damaging leak), multiplied over literally millions of apartments, means that those practices will hurt many people. Combine this with a very old housing stock (due to rent control that makes it difficult to redevelop buildings on the schedule that would happen everywhere else), and you have a situation where a strict plumbing code (and an enforced plumbing code) is essential to good order.
In cases where you are just doing one thing at a time that requires plumbing, you are better off hiring a good licensed plumber than some "contractor" who may just use some minimally-trained non-plumber to execute installation of things, leading to unsatisfactory results. Maccarone Plumbing in Glen Cove has a big practice in New York City, and they are licensed and uber-professional. I use them all the time at our house in the country and at client homes, and I see them all the time in my NYC neighborhood (UES). They are expensive compared to what some handyman would want, but their prices are fair for solid, licensed plumbers, and they are going to do it once and take the time to do it right.
UPDATE: Well, thanks to years of participation in this forum, my instincts as to things have become pretty-good. The NYC Plumbing Code expressly prohibits bottle traps. NYC Plumbing Code (2014), Section PC 1002.3(2). I don't understand from your description what needs to be done, but it may be also that because the vertical fall from the sink outlet to the weir of the existing bottle trap would be more than 24", he can't/won't just extend it. More likely, he knows bottle traps are illegal, and doesn't want to involve the building because the first thing the super will say is "bottle traps are illegal and you have to also remove the existing one".
http://www1.nyc.gov/assets/building...tors_and_Separators.pdf§ion=conscode_2014
Bottom line, just because your vanities are "beautiful" doesn't mean that they are appropriate for your location, or even legal for it.