How do you train the gluteus maximus without causing knee or SI joint strain?

Good suggestions. I would stick with the moderate range of motion and isometric exercises until you find out the specifics of her condition. i.e. due to a fall, muscle imbalances, joint/ tendon laxicity, microfractures, joint degeneration, etc. Also, being a yoga instructor she may be hypermobile and working on increasing flexibility might exacerbate her condition.