Sadmommy, hun, Pat (Fayerody) and many others here are trying to tell you that this man is playing mindgames with you.
Forget and dismiss this idea of a "second failed marriage!"
Starte thinking of yourself and your own needs, emotionally!
The very fact that his not wearing his wedding ring is a hurtful point for you is why he seems to refuse to wear it!
This is emotional abuse! (Of course, the type of man you have described could very well put it on as he leaves in the morning and then take it off! for the rest of the day!) He's emotionally abusing you, regardless!
I don't want to discourage you for seeking counseling...It's a good thing, but in my exp., counselors take time and will want to surmise the whole situation over several meetings before (and if ever) they give you advice! We, here on PC, are giving it to you straight! And from experience!
If you were my daughter, I'd be saying emphatically, come here to me...leave him!
Patty