Rather than filtering the water coming out of the sinks inside the trailer, I would filter the water before it gets into the trailer to begin with. Not only will that filter water for the whole trailer in a single location (vs. multiple sinks/filters), but it'll ensure that only filtered water gets into the tanks/lines, which is further peace of mind. Plus, nothing to install/modify, easy to use, etc. I use this Camco one:
https://www.amazon.ca/gp/product/B0006IX87S