Even if it´ll affects symetry (and I´m talking about a difference response in the low frequencies L/R speakers, maybe slight), the window will have a positive effect, because a lot of bass frequencies will "pass through" it (unless the windows are thick-soundproof kinda). Something that you can "force" (symetry on treatment) later with absorption in the opposite left wall. + all the treatment in the corners that will do the job. I think it´s your best option. I´m talking about treatment for critical mixing/mastering. Lots of very thick absorption (if rockwool) for excellent results (and you´ll need, for the square shape which excites same modal frequencies).Or tuned stuff, this is another conception, much more "tricky" to deal with/calculate, etc.
I´m not fan of carpet, I prefer hard floor/soft ceiling for both recording/mixing, but every room is different , you know, then it´s possible to achieve good results - but, if possible, take it out.
The other room (imo) is too small for (critical) mixing. Not "impossible", but worst.