I have been out of the education side of things for awhile now, so I am not current, but I think the only formal course work like what you are looking for would be at PSU (in Kansas). At PSU, we had 2 cnc classes, the first was to learn the software side of things, when I taught it, I based it around how I had learned things the hard way and tried to get them thinking about how to hold things so you could cut it, what tooling to use etc. The second class was to learn the machine(s) and apply the software to the machine. We had a 4 axis CR Onsrud and a 5 axis CR Onsrud, cnc panel saw and edgebander and now they also have a feed through vertical machining center. This was the sophmore and junior level courses with a furniture design class in the fall and furniture manufacturing in the spring of the senior year. These last two classes used the previous 3 years of coursework as a foundation to be able to use any of the processes to make the furniture, cnc being one of them.
I do not know of any courses outside of PSU and maybe the school I linked to earlier that would have it. There used to be a course in Atlanta at Georgia Tech, they had a program that had similar courses but I am not finding anything on them anymore. Their lab was based on machines that were on loan but still for sale by the machine builder so they could have a working demo lab.
Stiles, which is a large machinery dealer, may have some courses, they used to have an education branch. You'd have to go looking as I have not.
You may be stuck with trying to find a local manufacturer that has a router and see if you can learn from them somehow.