Is there a workout that targets conditioning of the rotator, strengthen the labrum as well.

The labrum is not muscle, and so you cannot strengthen it through exercise. You can strengthen the shoulder capsule to support the labrum and to make sure that laxity doesn't lead to injury there. A physical therapist can give you the right workout. It's mostly resistance work, using elastic bands.

Should be the entire capsule. Also, the labrum wraps the shoulder, so working only one side wouldn't protect it fully.

Do a search on Throwers Ten and Jobes exercizes.

Banding type exercizes is what you should concentrate on for the entire shoulder capsule/complex.

Balance between the front and back side is crucial as this keeps the humeral head centered within the labrum. Muscle imbalances often exist in the form of a strong front side and a weak back side simply because the front side tends to get worked more than the back. But this leads to anterior displacement of the humeral head and that, in turn, leads to wear and tear that can affect the labrum. So, do the band work others have recommended but work the back side more than the front.

This site has some good information. In particular, look at the links for "Labrum Injuries", "SICK Scapula", and "GIRD".