The 12 foot Jayco pop-up we just got rid of had a potty and a shower. (And refrigerator and 3-burner indoor/outdoor cooktop)
When we got it, you had to choose between an air conditioner or the potty/shower combo in the 12 foot units, but newer ones in the same size range (about the last 3 or 4 years) are coming out with both. I'm not quite sure how they manage it, since the 8" or 10" wheels they put on most of them are only good for about 1,000 pounds each (2,000 pounds per axle, roughly) and our old unit was near the 2K Lb axle limit (rated) when empty. Older 14 foot units (2 axles) may have both, and a little more room, if you're looking for a used model.
Some small units do use a "port-a-pot" that you have to take out and sit under a tree with; but the built-ins are typically a small (suitcase sized) cassette that you slip out (from the outside of the trailer) and dump into the nearest "stool" or RV dump when it gets full.
Quite a few of the newer pop-ups also incorporate "slide-outs" to expand the "living room" when you get to your camp.
The pop-ups are much easier to tow than any hardwall travel trailer. This is partly due to the lighter weight, but also due to the low height, which lets you see over the trailer while towing and gives much lower wind drag. The main disadvantages of pop-ups are:
1.) security - not much better than a tent - and an important consideration if you're carrying quite a few instruments(?)
2.) the limited life of the "canvas," good for about 10 years(?) but actually "replaceable," fairly economically if you've got the energy to do it yourself.
3.) cranking up and down everytime you want to get into it for maintenance during the off season (although electric cranks are available on some models).
3a.) In many areas, mine included, it's a constant battle with the weather to do off-season puttering with a pop-up. If you open it while the weather is damp, you have to leave it up until it's dry. Even a heavy dew while it's up means waiting for a hot, dry day to put it back down. Any dampness when you close up will result in mildew, which drastically shortens the life of the canvas. Even if the canvas is "impervious to mildew" (see the ads) the dust on the surface will get moldy, and will eat a hole in the adjacent fabric.
We did look recently at the "mini" hardside trailers like Scamp and Casita. We found that these generally gave you less space and convenience than comparably sized (and much cheaper) pop-ups. With most models of these "minis," you do as much "unfolding and folding" of the stuff inside as with a pop-up.
In "standard size" travel trailers, in the lower price ranges, we were very favorably impressed with both the Aerolite (see the Cub above) and R-Vision (which we bought). These appear to be the "lightest" towing ones on the current "new units" market (according to the spec sheets), unless you're willing to pay quite a bit more for one of the "exotics." There are a number of other brands that come fairly close for "towability," and your own intended usage may make other features more important.