She wants to keep you on the back burner, a plan B so to speak. You know what she means when she asks if you had any visitors over, don't you?
It is as she does not want you, but does not anyone else to have you either.
You were right in stating that it is tearing you inside. Do not worry that what is she is trying to reconcile. She is not, not yet anywayz... And do not go out hunting for other women of the opposite sex, because you are not ready yet, not by a long shot. Just focus on yourself and learn to be happy by yourself and learn to love yourself again. Contrary to what you've been told your whole life, YOU are the most important person in your own life and you take the least care of yourself. Go out, go hiking, do sports, be the best dad in the world. Focus 100% on the kids when they are with you.
Let your W go do her stuff and basically start listening to your gut feeling. I personally would not allow the hugs, as I am sure you are aware the hugs are as in a friend and not a lover. I do not want to be friends with the X, do you? How can you be friends with someone who treats you like that? I can't but that's just me. Sure you could be thinking that friendship is the way back to your W's heart, but I disagree...
Put your fears of the future on hold ,the fear is paralyzing you from moving forward. You do not have to move on from your W, but you do have to move forward.