When one of my computers is hooked up with an RJ 45 cable to the router (typically through a switch), YouTube videos will periodically pause and then restart; this never happens with computers that access the network through wifi, and stops happening when I change a computer from wired to wifi. What have I done wrong to create this situation?
The only possibility that your wired network is running slower than WIFI is because..
The possibility that that your cabled network has negotiate a 10mbit connection instead of 100mbit will not cause Youtube to jitter/delay... Why..
How to do some basic tests.
Open cmd line and type
If you have no dropped pings.. then your issue could be driver related on your OS.. does any other PC suffer the same issue on the same cable and ports?
How to check the connection speed of your network
You can also use this Utility to test yout network.
One thing that is very rare but did not even come to mind is Electrical interference. The OP's problem was solved when he moved his router away from the main transformer/power supply line.
As electricity does produce electromagnetic radiation, the CATx twisted wire was designed to pick up and remove it.. but in rare occasions (for example ground loop) the interference becomes interpolated with the signal and it cannot be removed, as the device thinks this is normal. Although not the same topic, this is a common problem in car audio enthusiasts, where there is a humming noise present after amplification. It is based on the same problem.
It sounds like your problem is the switch which adds an extra layer of hardware. What happens when you connect the computer directly to the router via a cable?