If you have two shore feeds, one going through an IT and the other not, you have a potentially dangerous situation on board. That was PROBABLY not original Hatteras.......
There's some good info in this thread and some not-so-good.
A quick primer on "split-phase" power...
The power in your house (but not necessaily at your office!) is what is commonly called "single phase." That's not really quite accurate - it would be more accurately called "split phase" for the outlets in your home.
The feed in your house has two "hots", each of which is 120V referenced to ground (earth), but they are 180 degrees out of phase. That is, when one is going positive the other is going negative. Thus, if you use both hots, you get 240V.
Ok, so how do you get "neutral". Neutral is actually not "neutral". It s technically called "grounded conductor". At the main service entrance panel in your house you have an earth ground which is a big fat wire or strap connected to the earth - usually via a rod driven (literally) into the ground. At that point - and only at that point - the white wire ("neutral") and ground are connected together. This is because in the us, power feeds actually use the earth as part of the system - on purpose! This was a design decision made when the US energy system was very young and it is not the case everywhere - Europe has a (mostly) "bifilial" system where earth is not intentionally used as a return path.
Now how does this relate to a boat?
In a number of ways.
If you have a system without an isolation transformer, neutral is carried from the main panel at the marina - it must not be connected to ground (safety ground) anywhere else, including on board. Neutral - or grounded conductor - carries significant current (potentially the same as either "hot" leg!) and as a consequence of wire resistance there can be material voltages on that line. Thus, EXCEPT at the main service panel for the marina, you can cause quite-large currents to flow if you bridge those two anywhere else AND create a serious safety hazard.
An isolation transformer normally carries only three wires in from the pedestal (assuming a 240V/50A system) - the two hots and the safety ground. "Neutral" is not connected at all! Safety ground goes only as far as the primary of the isolation transformer, and is connected to a "shield" around the primary windings, with the intent of causing the inlet fuse to blow if the primary were to short against the case. In this case shore "ground" is NOT carried on board to the boat's ground system - this is the true benefit of an isolation transformer, in that it makes the return path for any fault current LOCAL TO THE BOAT. That prevents you from both energizing the water (and possibly killing someone swimming near the boat) AND causing electrolytic damage to your (and someone else's) underwater metals. Without an isolation transformer a fault in ANY boat connected to the same marina's dock power can be carried back to the marina ground via YOUR boat, creating both a safety and electrolysis risk. The largest electrolysis risk comes from DC leaks, with the primary risk from AC leaks being death.
If you're running your generator - or you have an isolation transformer - then that device is an energy "source". As such a genset - or the secondary of an isolation transformer - must connect both "Grounded conductor" (neutral) and safety ground together at that point. In this circumstance you have no electrical connection to the other boats at your marina - faults in your boat cannot affect them, and faults in their boats cannot affect you.
This is why your breaker on the boat's AC panel (if you have a slide-lockout) for the genset has THREE breakers ganged in it rather than two, even though there are only two hots. Neutral must be correctly connected so that it either (1) is carried back to the dock if you have no isolation transformer and are on shore power or (2) is BOLTED to safety ground on board if you DO have an isolation transformer or are running on your genset.
If you have a system on your boat where an isolation transformer feeds house loads but you have a second feed line for certain things (e.g. AC units) you have a potentially dangerous condition on board AND you have completely defeated the purpose of the isolation transformer. While it is possible to set up such a "secondary feed" safely, doing so always destroys the purpose of the isolation transformer - so if you're going to do that, you may as well remove the big hunk of iron as it does nothing for you.
Instead, I'd replace the isolation transformer with one that can carry the entire load and run it all through there instead, and rewire the AC side to properly handle the loads on board.
Isolation transformers are such a safety "plus" that IMHO they should be mandatory for boats with shorepower inlets. Yes, they can be heavy, but being totally isolated from the dockside electrical system is both a safety and underwater metals protector, and IMHO is well worth it.