I'm really sorry to hear this GTTM. My situation isn't nearly to the point yours is but my wife hasn't had to face the fact that I'm apostate because we don't discuss it. I faded a long time ago.
I don't think you should feel it necessary to sleep on the couch and avoid most of the household rooms because she is not willing to allow you to be your own person. You have a right to your personal beliefs and so does she. Neither of you should punish the other for personal beliefs. It's my opinion that you feeling uncomfortable and avoiding her around the house and in the bed won't make things better, they just stress you out. Perhaps you should try a different tactic? Maybe you should make dinner and tell everyone, including her, it's time to eat and have the kids help set the table. If she doesn't come or doesn't speak during dinner you and the kids have a conversation and talk and just go on with your normal lives as best as possible.
That's just my advice but I don't know the details of your situation and I know it's so so so hard being in a house where you don't feel wanted.