Seems like you could try strengthening the muscles around the joints, but then again I'm no authority, and as previously suggested, I would talk with a seasoned teacher, or maybe even better a sports physiologist about how to do that in your specific case.
For side- plank, I would do it either with an elbow/forearm on the ground, or i would try bending the bottom leg at the knee and use that as a support with the knee and chin on the ground for support and less stressors.
If it was for plank and shoulders only, you could probably do a little bend in your arms to load the bicep/triceps more...
As for arms above head, is there a way to know when they'll dislocate, and stop before that? The meaning of for instance Warrior one, is to get a stable base and getting the energy from the ground up through the tips of the fingers. Stable base and reaching up, as stabilizes the center. The same feeling could probably be achieved with arms less than straight up.
If you're balancing in for instance tree- pose, would Y- shape arms work instead of I- shaped? That is with the arms up, but hands wide, instad of the "standard" arms up, hands together.
Many poses are designed for a specific purpose, but not all bodies are same, so making the same shape is not going to give the same resulting feeling for everyone. Yoga is generally more about feeling than the exact shape. Can you feel balance, rootedness, stability while balancing on one leg and expanding your body? Great! Maybe expansion is with arms to the sides instead of upwards?
It's very difficult to give more specific advices without seeing, so as pointed out earlier, see an instructor for a private session, and maybe also a sports physiologist.