Wow, that sounds so much like what my XW told me that it's downright eerie. She would say things like that in MC and the counselor would sit there with her mouth practically hanging open and would point-blank ask her if I was so great, then what exactly was the problem? She would respond "I don't know." I remember one time the counselor asked her if she loved me and she said yes, she asked if she respected me and she said oh yes, very much. She said what about sex, is he pretty selfish? And she said no I love the sex, in fact I would like to continue having sex. So then the counselor says "you love him, respect him and enjoy sex with him? In counseling we call that 'the makings of a great relationship!'" Then she asked again if my XW could describe WHY she didn't want to be married anymore, and she couldn't. To this day I don't know why we're not together anymore.
Is your W on A/D's? My XW went on them after our son was born 15 years ago. There are recent studies suggesting long term A/D use is making people lose the ability to "love". Over time they quit feeling love for their spouse and even their children. Maybe it's just me looking for answers where there are none, but I can't help but wonder if many of our sitches aren't the result of this.
Anyway I think you are right in not wanting to be her best friend. My XW kept pushing that as well, she didn't want to keep living with me but she wanted to be besties and kept emphasizing what great parents we were and how we would continue to be a team for our kids. I made it clear to her that I didn't want to be besties thank you very much, even though I would continue to work together with her when it came to the kids.
She's got to learn to miss you and that will never happen as long as she keeps living there (or in the back yard, LOL!) Maybe offer to build her a doghouse if she wants to live out back?