welcome to Vuo.
In Vuo terminology, what you call "patch" is a composition; not sure what you mean by "stage", but I suppose it could be a Layer.
This is an example of a way (not the only one) you could switch from one layer to the other.
I confirm that Magewell HDMI2USB device works to get a camera with HDMI out into Vuo.
BPMrotate node is missing.