Dennis @ PerfectForms
I would use a a Show Form object to open the child instance and pass two custom parameters. When the child instance opens use Set Field objects to receive the custom parameters. The First parameter should be whatever condition is required to move the instance to the next stage. The second parameter should be set in a helper field to determine if the child is being opened by the parent to move it to another stage. The value can be as simple as a “1”. Next use a Simple Branch to see if the helper field is empty. If it is not empty Clear the value in the field (so you can open the instance in the future) and submit the instance.
The instance should now be in the different stage.
The method I have described requires no interaction with the child instance from the user. Yes it does open. But the instance opens, receives the parameters, runs the behaviors, submits, and moves to the next stage all by itself. It is a few blips in the browser.
There is not way for an instance to change workflow stages without opening and submitting.