Is it common and possible to slightly reroute a drain/ vent in order to conceal it in the exterior wall?

As you can see in the picture I am changing the position of the bath tub and the position of the sink.
After asking around here I have come to the conclusion that I probably have a drain and a vent somewhere in a wall that I was planning to remove (shown replaced with a pane of glass in the second picture)

The third picture shows what I am assuming is the drain that I would like to reroute in order to conceal it in the wall for its basement portion. Is it possible to install a fitting that would push the lower segment of the drain into the exterior wall? so I can hide it ?

Here is the current layout

and here is the new layout

and here is how I believe that the drain is positioned
it also explains the existing wall between the toilet and the bath tub
this wall is blocking the light and it uselessly segments the space in the room

Update after demolishing the wall between the toilet and the sink

Existing route for the pipes

New route for the pipes