AC units help with humidity but if it is not sufficient you should use a dehumidifer instead of an exhaust, as you said you would just be pushing conditioned air outside. An air purifier would also be good for inside to filter the air.

A mini split heat pump would be perfect for this. As Vith expressed, use a dehumidifier if
humidity gets too high. (Get some hygrometers to keep track.) Excessive ventilation will only increase
humidity. Some added ventilation might
be necessary if the container is highly sealed.

In the Army we used large tractor trailer vans for some of our computer systems and they were old computers that were sensitive to humidity. The HVAC on the trailers was four heat/cool units mounted on the front wall (I've seen identical units on portable buildings).

The instructions for the system said that if you had a high humidity, moderate temperature environment, you may have to run one unit in heat mode and one or more units in cool mode to keep humidity down. I don't know if your situation is quite that extreme, but you did say extremely hot and humid.

Bruce

The Army used through-the-wall units? A variable speed mini split will work much better to control humidity under low heat load conditions.