It sounds like the transmission cooling line running thru the radiator failed. Cooling system is pressurized, which effectively pumps coolant/water into the transmission cooling line, which then gets into the transmission. The water /fluid form a "milkshake" in the transmission.
For expensive repairs a second opinion is always good.
The first thing needed is a new radiator and cooling system flush. You can have your mechanic put in a new radiator ( probably better quality than Nissans) and look at your transmission fluid while doing that. You'll probably save some money over the dealership on this work. He may suggest trying a Trans flush, or not. You will have to rely on his expertise there. Good chance it's too late though.
You mentioned "Copay". If that means you have an extended drivetrain warranty, it is probably not a Nissan warranty, but an aftermarket warranty. If that is the case, your mechanic can probably put a rebuilt transmission in and bill the insurance company. That will cost less than the dealer, probably by a fair amount, so your copay would be much less. Those warranties typically let you select the mechanic.
You can go used transmission. Log onto car-part.com, enter your vehicle info, select the correct transmission type (AWD, 4x2, etc.) and you will see used transmission prices. Probably figure 750.00 to 1000.00 labor to do a swap, depending on you mechanic, locale, etc. Those will typically have a 90 day warranty, parts only. If it fails, you get a replacement used transmission free, but you must pay the labor again. You would let the mechanic buy the used transmission himself - he will tell you what warranty he can give you.
Or, you find a shady looking character named Guido, hand him 500.00 and the keys, and tell him you never want to see the car again. Wait a day or two and report it stolen.
), but was not counting on this. Do I have any other options? ie:
unfortunately, that really is your best bet.