Some of the parent portion of the game should be doable while the parent is with the child and it might even serve to distract them from watching needles being inserted, etc. The visualizations should not be too realistic, and the child or parent needs to be able to flag concerns to be discussed with a provider. Here is a hypothetical example.
A child comes in for kidney dialysis for the first time. They are in pain and the parent is worried about that and paying for the expense. You need from the child to know exactly where it hurts and how much. A 10 point pain scale is alien to them and too abstract, so instead you take advantage of the fact every child has been hit by a sibling or playmate and you show images of from tiny insects to large animals hitting cartoon characters with the relative size being the proxy for how painful the impact will be. Then to show location have the child move different sized stars to where it hurts on the image and blink the star chosen or use it as a building block to a solution image like a home for the character. The game must be able to take into consideration individual known differences in organ locations. Each major procedure would need to have its own scene. For the parents let them scan their own insurance cards instead of waiting for a clerk. What I most hated about hospital experiences was the uncertainty such as being given no idea how long the wait would be, not knowing my rights to be treated elsewhere, not being given any information about surgeons such as after a car accident but offered take it or leave it. Most of all I hated waiting, and I could have used my smart phone to enter all the required details without waiting. Only clear cut. life threatening emergencies are seen right away. My second biggest hate was having to answer the same questions over and over again for entry into different computer systems that did not talk to each other but could have printed and scanned the data without me. Ask a question only once if there is no suspicion of mental illness or dementia. Re-asking makes it seem like the prior efforts were a waste of time or you are searching for some vague right answer instead of fact gathering ONCE and asking if anything has changed..
Any of the computer gaming companies have what it takes if told the info to collect and the details of what must be conveyed to parent and child. They need not use the same terminals to play together. Pilot the idea with a simple surgery to test feasibility. Remember cartoon characters don't experience pain, but they may need to in order to understand how to ask for pain specific help.