We dont own a pup, but we do own a 37 ft. Wildwood travel trailer with a bunk in steamy humid Florida. And, when rainy season comes, or if it is really humid outside, condensation is a problem even with a larger TT.
Our solution at first, which may work for you in a pup, is to get those small dehumidifiers like Eva-Dry, some of which are just calcium chloride, and a few of which run on 120V AC, and can be set up for continuous use.
We used to use these plastic bucket passive dehumidifiers for our TT, but found they were not enough, so for the last few years, we have used a 120 VAC powered 45 pint GE dehumidifier, which is left plugged in 24/7 and set to 55% RH.
We set it up in the shower when we leave, with an extension cord (yes, the shower is dry) and the drain hose feeds to the shower drain. So, the interior never gets too humid and no mildew grows.
Before we installed the dehumidifier, one weekend we arrived and found mildew growing on every surface from the floor level up about 2 feet. It took a while to clean up every square inch inside the TT. So, we bought the dehumidifier that weekend. Sure, our monthly power bill is an extra $30 more than it would be at our weekend place, but given the thousands we spent on the travel trailer, it makes sense to keep it clean and dry.
Further on preventing mildew and odor, which can result if condensation builds up in any RV, there are products that contain stabilized chlorine dioxide (sodium chlorite), which when humidity increases releases a mild form of chlorine gas that will prevent odors from developing in your RV, pup or trailer. They are sold in the form of sachets that you hang up inside the RV. When the humidity increases, the chlorine is released and the inside stays fresh. It does not damage any fabric or materials in the RV, and we have used them extensively and often. Here is on the those products on Amazon:
hope these ideas are helpful to you. They work in sultry, steamy Florida, and are unnecessary in northern climes where humidity is not an issue. It's an issue here, 10 months out of 12.