Right side shakes when appling the brakes

Both solutions are correct.  In the future, be careful about driving through standing water (rain runoff).  If the rotors are hot (from normal use) and are then doused with water, they can warp, causing the vibration you feel when applying the brakes.  Warped routers can cause inconsistent braking on one side or the other, which can be dangerous.

SM124 is correct. I would machine both at the same time so that they are in equivalent shape - same with replacement. They should be close to the same condition anyway.

I would also consider if it only happens when the brakes heat up. I read that the rotors for these vehicles warp easily and when mine warm up, they throb (not ABS BTW). When cold they are smooth.

Sounds like the right side rotor is out of round.Either have it machined or replaced. Also when checking the rotor make sure the steering linkage is good at the tierod ends. You should probably have both rotors serviced at the same time