To get started, take a look at this gallery of images related to setup, bowhold, and simple solutions for teachers and students.
So here's the deal- when students have hypermobility, it means their joints are unstable because they don't have a normal end range. When you then ask unstable joints to support weight or articulate, you are putting undue stress and strain on the joint and just continuing to ask the ligaments to do the work, rather than strengthening the muscles to support the joint. What we want to do is strengthen the muscles as much as possible, and then add load. The easiest way to do this is take the instrument away and isolate specific joint issues. Many PT's use theraputty as a great way to get specific finger strength (it's basically a denser version of silly putty with different resistance levels). This would be great to have on hand in studio (no pun intended) and add to your weekly lessons, especially with growing kids. The most important moves to focus on would be the finger pinch, keeping the fingers curved. For string teachers working with wayward pinkies, I like this video about using a clothespin for resistance- also a great idea. (Also, take a look at how to teacher kids to hold pencils- great if you're a parent!)
I'm also a huge fan of bow hold buddies, especially for young children. This creates a pinky nest to help curve the pink, as well as provide a nook for the right thumb, especially if it locks out usually. They also make something called the "cello-phant" which looks interesting.
For flute, clarinet, etc., I've also seen finger slings/rings/ etc, that can help to train the joints to stay bent and start to strengthen the muscles. Also ask the student to look at how they type, text, hold a pencil, etc. If you can cultivate even a smidge of awareness in daily life, there can be huge transfers in a musical setting.
The bottom line, is that continually locking out the joint puts strain on the joint, can lead to osteoarthritis, pain, and other issues, and that the surrounding muscles are usually weak and can't support the movement being asked. Some people live a full pain free life with hypermobile joints, others deal with osteoarthritis early in life, or are diagnosed with Hypermobility syndrome. Helping students (or yourself) can improve your performance and prevent future pain.