OK. Just so you know, you confused me too.

It sounds like you wanted an HDMI matrix (2x2) but then you talked about sending 'AND' receiving thru the same device. How would that even work... physically. Things have to be hooked up either as an output or an input.
So to answer your original question as you wrote it = no. Either you have a HDMI switcher that is 2x1. Or you have an HDMI splitter that is 1x2. It can't do both.