An old-fashioned board game approach, inclusive of new and interactive technology, wherein "patience" by the "patients" can be acquired/rewarded/paid with "shens", a tangible/or possibly intangible unit of currency/toy/activity/etc.
The "game" would commence upon the child/children ("player") requiring medical attention; the first "move" would be arriving at the facility for care. Waiting areas would be "fueling stations", where, dependent on age, "shens" could be acquired by building, drawing, singing, quizzes/tests/mind games, etc. Hallways would be !' colored-coordinated as "paths" to next "challenge": treatment. "Allies" are medical care personnel; "obstacle" is disease/condition.
"Shens" would be traded/spent for ....(dependent on facility/disease/condition/etc, and what would be deemed an appropriate reward/compensation for patient: food, person/people/clothing/autonomy/access to other areas/etc.)
"Allies" also can reward more SHENS for courageous conduct (enduring painful, invasive tests and treatment), for displays of quiet patience (waiting for staff, meals, etc), responding to treatment (only to encourage a positive attitude, which has been linked to quicker recovery; conversely, if deterioration occurs, SHENS should be encouraged through "fuel stations", which in turn can contribute to happy, positive patient), and other ways not herein addressed.
Another inherent possibility: to prepare the patient to navigate and benefit from the health care industry, SHENS are desirable to attain, as these can be used to obtain "better" healthcare. Because SHENS can be acquired by all, with no bias or prejudice, with impartially set parameters for payment related activity (drawing vs singing vs patience), competition and exclusion should be eliminated, fostering patient to patient support, teamwork, equality, and dignity for all. PAY SHENS for access to.... (again, dependent on institution, medical staff-deemed-appropriate rewards, etc.).
"Winning" is defined by successful navigation to "Finish", whether that is departure/release from clinic/institution/treatment/etc., and possibly with an adjustably set goal of SHENS, patient dependent (whether Player set, or parent, or medical staff).
Not herein addressed: punitive measures for conduct. While acknowledging that games commonly have, even dictate a necessity for, losers, the intent of PAY-SHENS "board game" is to limit--eradicate--competition between players, and animate all to "WIN".
Also to note, the environment and 'game' should be instituted with minimal change to existing structure, staff practices, methods of treatment, etc. Further, it should be created with enough incentive to involve the patient, but not so enjoyable that patients would self-injure to become/remain a player.
So, my idea probably needs more fleshing out than my one mind, my limited experience, could provide!