Rotator cuff stretch causing discomfort

I’m trying to determine why I feel discomfort with a specific rotator cuff stretching exercise, and why I have somewhat limited mobility in that same (right) shoulder. The stretch that causes some minor discomfort is the one where you reach across your chest with your arm, placing your hand/wrist over the other shoulder, while using your free hand to pull the elbow towards you.
If I do this with my left arm there’s no discomfort.
With my right arm it is a little unpleasant but I would not call it painful. Also, when I do the “towel stretch”, I have limited mobility.
With my left hand I can reach back and touch my middle back without a problem.
My right hand however cannot reach as high on my back.
I can use the towel stretch to pull my right hand to my middle back but this too causes slight discomfort. I stretch my right shoulder every other night or so but have not seen any improvement in my mobility or a reduction in the discomfort with those stretches. I would like to know which rotator cuff muscle(s) cause this and what else I can do about it.
I’d like my right shoulder to be fully mobile and free of discomfort like my left one.