From personal experience, I have been using the Reformer to keep my sometimes problematic shoulder strong in the following ways:
I agree, definitely do some warmup, maybe holding a weight down by her side to open up joint capsule. Two things on the floor for warmup are (1) “cactus” arms and snow angels, with no load at all. Your client can also do these range-of-motion exercises standing against the wall, with spine pressed toward the flat surface. Emphasis should be on external rotation at the shoulder joint, extending the arm away from the body and moving from the scapula instead.
(2) Elbow plank, progressing from knees to full plank on toes to address serratus weakness. (3) Plank on knees, simply widening and narrowing shoulder blades. My orthopedic surgeon friend calls these “pushups plus.” He suggests a shallow pushup followed by a rounding and stabilizing ont he upper back. These may be too hard to start with, and should be done against the wall for less loading.
I find the Pilates chair to be difficult for people with shoulder weaknesses, and use the Reformer more with them. They can do Mermaid seated on the chair, however, because it involves pressing the bar down–if they can focus on the movement or pressure coming from the shoulder blade instead of the shoulder joint.
The Reformer exercises I recommend are kneeling facing away from the footbar, on a very light spring, doing “Chest Expansion,” which is really a lat pull-back, again addressing the serratus and scapular stability, as well as balance. Sseated cross-legged on a small platform works, too. Try the exercise with crossed ropes also. The last one is rotator cuff sweep with crossed ropes.