How does the PCS process work for a Reservist married to an AD service member being stationed overseas?

Look for an overseas reserve unit and call them to see if they’ll accept you. There are units in Europe, Korea, and Japan. Another option may be to get constructive credit with an AD unit through your current unit. Another option may be to request a transfer to IRR

Same process for any spouse. Get married before the PCS and you'll travel with her PCS move overseas. When or before you arrive search for a compatible army reserve unit where your spouse is stationed. It will be much trickier if you wait until after the PCS to get married.

Good luck, and then there is the whole part about finding a civilian job while overseas....

When I was stationed in Europe, our unit had a couple of reservists that would do their monthly drill with our unit. They were aviation operations and it worked perfect because once a month they would relieve some of our personnel .
I know in Germany the reserves have a mission support command.

https://www.7msc.army.mil/About-Us/