Just to clarify, I am not suggesting you go soft. I am saying you need to get your priorities in order. First on your list should be protection (physically, mentally, financially. Etc.) of your children, as well as yourself.
Have you chosen a FT and made an appointment? Have you received legal advice? Have you taken steps to protect your finances? Established an activity schedule around the kids and some type of visitation schedule? You will need to decide if their mother can come to the house to visit and how that will be handled. See where you stand legally and look at your options.
As she said, she is obviously confused about your signals, and that is why you need to give your attention to the most important things first........before you jump into exposure and those type issues, but that's just me. Starsky's experience was more extensive and he can advise you better than I can.
Remember, you are not dealing with rational person. You better be serious about your decisions b/c you will be playing with fire! Never think she wouldn't wipe you out financially, leave with your kids, or anything else she may decide. That is why I said to use wisdom. And you have to admit, you have let your emotions dictate your decisions up to this point.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!