I actually had a scenario similar to this one. Not exactly the same but similar. I was the instructor on a KC-135 taking off out of Okinawa, Japan to go refuel some fighters in South Korea. My "co-pilot" was actually an aircraft commander who was getting ready to go to instructor school and flying in the right seat, after not having flown on that side in a number of years. IFR with thunderstorms in the area we noticed that his heading was displaying 11 degrees off from mine. We trouble shot the problem down and decided to re-align his inertial navigation unit. So my "co" turns the power to standby on the #2 INU (his side), but then put the #1 INU to align mode. Basically, he turned em both off, and we lost ALL of our navigation ability in the weather. We still had GPS and VOR signals coming into the airplane, but since all the heading info comes from the INU's the jet had no way to display the info. We were also down to our last backup attitude sources- the autopilot attitude gyro and the standy ADI.
Here's what I probably should have done: Requested no gyro vectors to an ASR, and declared an EP.
Here's what I did: knowing that we'd be without nav ability for the next 8 minutes while INU 1 was performing an airborne alignment, I told center we needed 20 miles left and right deviations for weather. I told my co to fly straight along the current heading off the whiskey compass (since our next turn was still a ways away), and I re-aligned INU1 and then INU2. We got all our systems back, and then I proceeded to belittle, make fun of, and generally browbeat the co!