Water leaking when we are away for a few days
(Not going to be as helpful as I'd hoped, but maybe helps you think of something you hadn't thought of)

Since you mentioned the kitchen is right below, I'm going to assume finished walls/ceilings and that you can't easily trace the pipes(or maybe you're lucky and it's a drop-tile ceiling?).  

I've heard of a few ways to find a leak, but they almost all involve being able to reach the pipes - either to spray something like dish soap on them and watch for bubbles or put an improvised stethoscope(flat-head screwdriver, usually) to them so you can listen for the leak. 

I've had both tub/toilet gasket go and not be obvious for a few days (wood subfloor wicked the water to about 4ft away in both cases), so that might be something to consider too. 

Either way, there's a pretty good list of steps to try here:
https://www.plumbingsupply.com/how-to-check-for-leaks.html
Most of it depends on having access to the piping though.  

Having said that, unless the local plumber has a camera s/he can fit down the copper pipe (?), they're going to have to make holes too...