First, 37 ... DUDE that is YOUNG!!! I wasn't even married by then. You've got a whole life ahead of you. OK, maybe not whole, but more than half!
I agree w/ much of what Zues wrote. Maybe anxiety is a big deal w/ your wife but so is her anger. I think you provoke her anger by being overly friendly. I think it makes her feel like you're not really seeing where she is emotionally. It makes her feel disrespected and disregarded and not heard. I would honor her wish to have emotional space from you.
About the house -- it doesn't seem all that crazy to me to rent when you're teetering on divorce. I suggest you just give her what she wants: OK, let's find a good rental and sell our house.
It just feels to me like you're trying really hard to save the marriage and it's coming across too obviously and strongly to your wife. I think it feels like more than pursuit to your wife, it feels suffocating.
Me: 50, MLC/WW 45 Young kids Nov 2015: BD1 Apr 2016: BD2 Jan 2017: W filed Feb 2017: D final