I know people with the Yaris. I'm thinking wet bath and tow capacity of said vehicle are a bridge too far.
There are some ultra lite teardrops and motorcycle sized pop ups that would be within a more reasonable weight
for a Yaris.
For a shower there are battery
powered pumps that heat water using one of those disposable green propane
tanks. Small compact and light weight
. Fit in a small bucket used to hold the water. One of those and a phone booth sized tent with mesh floor made to be an outdoor shower might be an option. Another few years I'm going to need another size reference, who will still know how big a phone both was?
There are endless debates about towing capacity exceeding, not exceeding, dire warnings and counter arguments. It is essentially really simple if you push the limits you have to do so only to the point where you (personally) can still do so safely. Yaris and 1,500 lbs. of trailer is at the least a very demanding challenge to do safely. Not to mention the repair costs that the additional wear and tear are sure to require.
Would be cheaper, safer, and a lot more relaxing to pick up a used vehicle with a towing capacity sufficient to deal with the trailer you actually want.
The best explanation backed by actual data I have seen for why Europe and US have such different towing specifications from manufacturer is speed. How fast you go has a huge impact on stability and ability to stop. In Europe the speed limit for a trailer tow is much lower, and the fines are huge for speeding with a trailer. Assumption is vehicle will not exceed that speed. In the US we not only have higher speed limits for towing there is also the presumption that we will drive over those limits and closer to the flow of traffic speeds. Speed has a profound effect on stability, there are other factors such as trailer brakes
being required, special drivers licenses etc. in Europe but it mostly dovetails with the degree of difference between our speeds.
Just don't overwork your guardian angel with your tow/trailer combination.