I drove my 2007 GL450 on a 1500 km trip, and midway the car started having acceleration issues. It became very sluggish, shifted hard, and wouldn’t accelerate even at high RPM. At low speeds, the engine was also shaking.
When I reached my destination, I noticed the coolant looked like a milkshake (as shown in the pictures). likely due to transmission fluid mixing with it.
I’m in a remote area where there’s no replacement transmission cooler available. Is it possible to bypass the cooler temporarily and drive the car back to get it replaced?

Yes, for emergency I would. But your trans is likely running on water so a flush is in order.

It may go to limp mode anyway if is senses trans fluid temp too high so you’re still driving a lame duck.

Are you certain that is transmission fluid? The transmission oil cooler is inside the right (passenger side) radiator tank. It is physically isolated from the coolant; it is a heat exhanger surrounded by the coolant. The transmission fluid lines connect to fittings on the right radiator tank. Of course, it is possible the heat exhanger failed. If the transmission fluid heat exchanger has failed, coolant will leak out if you disconnect and bypass the heat exchanger, so this is not a sustainable solution.

A few GL models have an auxiliary transmission cooler in front of the radiator. I do not know whether in these models the radiator transmission cooler / heat exchanger is still utilized. @Max Blast is this a EORP feature?

Another possibility is that engine oil is entering the cooling system, either via the oil cooler (another coolant heat exchanger, located on top of the motor) or the head gasket. The oil cooler can fail, and leak oil into the coolant, or much worse, vice versa.

Check your engine oil for coolant; in that case, the oil will be milky white. Do not operate the engine if that is the case.

There is another possible path for oil to get in the coolant, and that is power steering fluid, which could enter via a similar heat exchanger on the left (driver side) radiator tank. Check for coolant in your power steering reservoir.

The hard shifting does not necessarily mean there is coolant in your transmission. The transmission control module could be attempting to compensate for your struggling to get power out of the engine.