What are the issues with your place? Do you live with friends family an ex?
It's great that you understand hanging out at her place as an escape it contributing to the problem. Definitely focus on improving your own home environment so you can retreat to somewhere where you can process, reflect and get some peace.
As far as marriage it may be an overall general long term goal, but this situation doesn't seem to be stable enough for that.
Your GF seems a bit too controlling so reclaiming your own turf is a practical first step rather being a guest in her place and just tuning her out. This seems to contribute to the overall issue of being shut out.
While your sessions are private, she seems to want to be able to have conversations with you and perhaps thinks she's not privvy to any of your thoughts and feelings but your therapist is. Unfortunately you're creating a sort of competition for your attention, energy and feelings.
But you can change that by not hanging out as an escape. Please try to explain that you're just processing things and try to communicate better rather than showing up after therapy and just withdrawing.