I say bathroom. It looks like it needs it more. I know you want to keep fixtures, but I'd ditch the pedestal sink and go for a small vanity. There are Euro-style ones with small cabinets under the sink.
Since your son is a child, you may also want to update to a single lever control that has scald protect. That would bring it up to code and ensure that the water wouldn't get hot enough to burn him.
Delta makes a handle with two levers stacked on each other (
Lahara dualstatic) that lets you control pressure and temperature separately. Requires a Delta Multichoice valve. They come in threaded, ones needing copper sweated, and pex barb. My friend has one and it's good. I'm putting 2 of them in my house.