I'm not sure it matters, as magnesium won't repair a rotator cuff separation. No supplement will. If you take too much magnesium bit itself, be careful, because taking too much can leach the calcium out of your body so if you do supplement with it do it with knowledge. Magnesium can relax muscles if you have cramping problems, and along with calcium it helps build strong bones, but you are talking about something else here. If you don't need surgery, you should probably get yourself sent to physical therapy to see if they can help with it. The best way to take it is with a meal. The citrate form is good because it adds acid, but there are several forms considered well absorbed. The one to most avoid is the oxide form. Also, avoid eating any of that dairy you're working around -- dairy increases inflammation. There are some supplements that are supposed to help with joint and connective tissue, such as collagen, glucosamine sulfate, and some others. Others help with inflammation, such as turmeric and ginger. I just don't think magnesium is one of them and if the rotator cuff is torn severely enough you'll probably need surgery. If it's just age and usage, again, you'd probably be sent to PT.
You should take Vitamin C and vitamin E it can help in reducing the pain.