Yes they believe we are obsessed with them, that they can come back whenever, and we will take them back whenever. Prove them wrong.
I proved her wrong when she was still "deciding" to leave me (and the children, though of course I would fight for nothing less than 50/50... they may be the only thing that is keeping her on the planet right now, which sux for them, they will find out later). She admitted that I was trying 110%, but that she wasn't sure if she could get the love back. To me that meant "no." She threw out, "what if this happens again in 3 years?" To me that meant "yes." So I proceeded to check if she was lying to me, and she did, then lied to me about lying. I then told her that a relationship was two people, and that it wasn't just her choice if she stayed or left--- even though she has been putting on her friends and family that it was her that stayed so long trying to work it out (me: really? HOW?) for the kids.
So I said, "I think you need to leave. It's done." Things changed after that. She locked her phone, went back to checking her secret email account (a behavior she did before she met me with one of her ex's, she showed me and deleted it at the time to prove that she was over him). That was the boundary I drew. I will never, ever take her back, even though several people think she will want to at some point. Now I know what I am dealing with. She would have to get SERIOUS, specific help for me to even consider it. But no, probably not even then. Just my stupid 1% fantasy. The kids make it hard. If it weren't for them, I'd have already evicted her, or she would have most likely just left. I give a 25% chance of a suicide attempt at some point when her current/new guy leaves her, especially with her winter depression coming on. I need to get her away from me, but carefully and legally due to our children.
I think on some level she knows I will never take her back though. And that gives me some relief, perhaps.