I don't enjoy MRIs in particular. My question is can shoulder and hip be done at the same time?

Not literally at the same time but maybe possible as consecutive examinations undertaken within a pre booked time slot.

Potentially laying 2 hours in the tunnel? Even less pleasant outlook!

From you user name, I'm guessing you're in Phuket, so not sure if this is practical, but here goes:

If you find the narrow enclosed confines of the traditional "tube" MRI machine unpleasant, find a hospital that uses an "open" MRI machine. When I ruptured a disc in my back, I went to BNH (Bangkok) Spine Clinic and they needed an MRI but I had panic attacks upon entering the machine. They transported me to Urupong Hospital (Bangkok) which had an open-style machine.

IF there is no urgency for your MRI scans and IF there are no open-style machines in Phuket, maybe a quick trip to Urupong in Bangkok would be worth it?

While I consider myself only mildly claustrophobic, the machine at BNH was so narrow my shoulders were slightly squeezed and (and this was the real trigger) I could feel my breath bounce off the top of the tube.

I'm patient of BNH & know want you mean. Excellent hospital anyway

The MRI inside tunnel set up is very low and not easy to enter and it causes Claustrophobia to many people particular for men.

As a result of the the MRI low tunnel set up many people use the CT Scan to get some outline of the body and the brain, but the CT Scan does not entirely outline the same procedure as MRI does.

I have had both traditional and open MRI's. I opted for an open one once, because I am claustrophobic. Unfortunately, there is not much difference. The open machine is only open on the sides. The upper part of the machine is still so close to your body and face, that you are pretty much pinned between the table and the machine. The only way to really have a stress free MRI is if you are having something scanned below the hips. Then they can put you feet first, and just partway into the tube. Anything above the waist is going to be unpleasant.

I have had both traditional and open MRI's. I opted for an open one once, because I am claustrophobic. Unfortunately, there is not much difference. The open machine is only open on the sides. The upper part of the machine is still so close to your body and face, that you are pretty much pinned between the table and the machine. The only way to really have a stress free MRI is if you are having something scanned below the hips. Then they can put you feet first, and just partway into the tube. Anything above the waist is going to be unpleasant.

The open MRI machine at Urpong Medical Center in Bangkok had no upper part. I can't recall how high the sides were, but they were low enough that it induced no anxiety in me. There must be quite a variety of MRI machines out there.