Shorepower issues

The difference between a 3 and 4 wire cord is simply that you aren't carrying the ground with the 3 wire version, only 2 lines and 1 neutral. Your ground is isolated aboard from shore. You could just as easily use a mare standard 4 wire cord, as the ground is transferred through the round metal portion of the plug housing. You still have only 3 prongs, 2 for line and 1 for neutral.

It's a bit hard to understand what you're facing as we don't know how your shore power feeds your panel system in comparison to how it is fed by generator.

Check your battery chargers. The input voltage should be listed on the identification plate. Why one is 12o and the other 240 was likely someone thinking they were trying to balance their load. Good idea to simply do the math of amp requirements for each circuit on each line of the panel. Listing that information out on a piece of paper will help you to better understand the existing load balance, requirements, and path to managing the loads so that you can run the priority items.

The isolation transformers are simply stripping the ground from shore and allowing the vessel to use its own bonding system, separating it from the shore circuitry.

No. You can only run 50 amps through a shore cord rated for 50 amps. To use a smart Y you'd need heavier cable from the pedestal all the way to your panel's main breakers. And then you'd need apparently to reconfigure the incoming power on your panel. Your panel appears (from the shore side) to be separated into groups allowing you to manage and spread the load. Best guess is that it was set up properly and you're simply going through your learning curve of how to make it work.

What did your surveyor tell you about this setup? Did he review and comment? If he didn't, and if you're in Ft Lauderdale, you might consider having Wards come out and do an electrical survey and provide you both with their review as well as their interpretation and advise. You'd learn a lot during that process of both how things work in your setting as well as what their recommendations are. Bad power setups are a big problem both for you as well as for the boats around you.

Sarasota, consider calling JTB out of St Pete if you don't already have a resource.

Also, reading back to your initial post, your boat should likely be set to allow you to run one AC on the one cord. I can run most of my systems and one 5 ton chiller on a 50 amp service (can't cook, too). If I need the other chiller, too, I need to run off my 100 amp setup. If your main cord plugged, does it provide power to only one chiller or to all three? I'm trying to get a sense of how your AC side is set up to distribute incoming power from shore...

Isolation Transformers take 230Vac and make 230/120. It makes it's own neutral.
Fault current from the transformer to shore is still (always) required.
This makes the 3 wire shore cord (No Neutral wire).
Onboard, Fault current may be released to the bonding system and the water or tied to shore.
I like the idea of galvanic isolation and a tie to shore if divers go under your boat often.
PM me for some schematics if needed.

I don’t know if this is applicable to your issue but on my 50amp shore connection I had lots of trouble with the wiring to the shore power receptacle on the boat and the twist lock plug. In fact, one time I lost shore power and pulled the receptacle and could clearly see burn spots. I replaced the boat’s receptacle and the boat end plug on the cord with a 50 amp Smart Plug. Huge difference. No issues since, cord doesn’t get hot and I’m able to run more by having a much more solid connection in that plug and receptacle. It’s also easier to plug and unplug. I would gladly pay to change the marina side as well but they won’t let me. And no, I’m not a paid spokesperson or dealer for Smart Plug. Just very happy with the product.

Hmmmm. I meant two hots/ one ground / no neutral

Wrong. I know my earlier typo made things even more confusing but with isolation transformer the shorepower cord carries TWO HOTS and GROUND. it does not being neutral on board as neutral is created but the tranaformer(s)

Isolation transformers work in precisely the same manner as polarizations transformers, they ensure proper polarity regardless of dock wiring, with one important distinction; the dockside green safety grounding wire is isolated from the vessel’s green safety grounding, bonding, or DC negative wiring. Why the separation and what’s the value and risk to such an arrangement? The isolation of the grounding systems achieves one additional goal for an isolation transformer—it reduces the possibility of “foreign” or other boat-induced stray current or galvanic corrosion.

More correct word would be "may".
The green wire to the shore service can be configured different ways.
Total isolation from the shore service makes any fault current to release thru your ship to the water.
We encourage the idea of galvanic isolation and a tie to shore if divers go under your boat often.