A true Wikipedia reference-linkfrozen shoulder is frozen due to an Wikipedia reference-linkadhesive capsulitis. Shoulder impingement, or shoulder movement inhibited by pain or weakness are different problems, and can be sorted out by mobilisation of the glenohumeral joint or cervical mobilisation of the Wikipedia reference-linkfacet joints, respectively.
Evidence based medicine suggests that adhesive capsulitis is made worse by mobilisation techniques, whether it is gentle or very firm.
The only way to sort out the problem is to 'unstick' the capsular adhesions, which is done using a technique called glenohumeral capsular hydrodilation. The technique involves an injection of local anaesthetic around the upper shoulder, then a saline solution containing a small amount of short acting anaesthetic and very low dosage corticosteroid is injected into the shoulder capsule. The Doctor injecting the solution can feel the resistance of the capsule against the syringe plunger, and the resistance can suddenly give way as the adhesion frees. There may be more than one adhesion, therefore the Doctor continues to inject the saline to a maximum of 40 mililitres in an average sized person.
Following the procedure, and whilst the anaesthetic continues to work, the patient should move the shoulder through the maximum achievable range of movement, and should do pendular exercises for a few days post procedure. If a therapist is available, passive range of motion should be attempted as soon as possible after the injection, preferably immediately after injection.

If a patient has very limited internal rotation (hand behind the back), limited active and passive flexion, and cannot easily lay on the affected shoulder at night, plus has had the symptoms for greater than three months: they are ideal subjects for the procedure.
It has become popular amongst radiologists to do the procedure with X-ray guidance of the needle, however I have found better results from a Doctor with good anatomical landnmark and palpation skills, doing the injection in rooms. The whole job can be done in less than 20 minutes, with significant pain reduction and increased range of movement. The patient may or may not be in pain afterwards, but must continue to move the shoulder to avoid the redevelopment of the adhesions from the newly raw areas. Pain medication to allow for pain reduced movement is a very good idea.

The technique does not work if there is a capsular tear, as the fluid leaks out with inducing sufficient tension to remove the adhesions.
If you can arrange the above technique, you and your patients will be amazed at the results. The condition must, of course, be correctly diagnosed before attempting hydrodilation.