I agree with that Chuck. I suspect neglect vs abuse but you could argue neglect is abuse....
There are so many red flags to me but legally she has joint custody so I can't focus on that. Kids are getting older and outspoken. It will work out. They won't tolerate it forever. Hopefully XW does some soul searching. I just wish she were excited to be a mom and not treat it like a chore, like taking out the garbage. I think being a parent is awesome!
I'm painting my daughter's nails, French braids, fish tail braids, you name it. I'm into all of it.
So, I read through your thread quickly so I apologize if I've missed anything pertinent.
First, as a victim of abuse as a child myself, don't think that just because your kids are getting older and more outspoken that things will work out. Even if they don't tolerate it forever, they will carry it with them forever if it continues and they don't get the help they need. I come from a family of five siblings, and two of us are severely mentally damaged to the point of it affecting their ability to live life. You've described how your kids pee and poop in public so it's a safe bet that they're not learning healthy coping mechanisms.
It's fantastic that you think parent is being awesome, but I think you need to keep fighting to find a way to remove her from the equation as much as possible. I know you've done a lot to this end already, but your kids will thank you for your persistence. She likely never wanted the responsibility of being a parent (just like my father didn't) as you point out and there really is very little worse than that. Being around that form of neglect destroys your self-esteem.
In terms of the emails she has sent you... that's the real pickle from my perspective. She wants to be back with you and the family and as long as she doesn't have that, but wants it, her behavior will persist. At this point, she's conditioned to know that if she neglects your children or lashes out that she'll get a reaction from you. From her perspective, reaction=interaction, which she hopes will lead to reconciliation. It's twisted and dark and upsetting, but I think that's how she's trained her mind to deal with this in an effort to get what she wants.
Just my advice, but I would respond to either the email she sent asking for forgiveness, or if you prefer to wait for the inevitable next one, respond to it. I'd give her the forgiveness she's seeking but make it clear that the relationship is over and that you both need to be there for the kids. If you ignore, ignore, ignore... well, you know at this point what's going to happen.
I'd be right with everyone else telling you to ignore her if kids weren't involved, but they are, and it seems like she leverages them to hurt you and force contact. I wouldn't be surprised if her clouded mind believes that all she needs to be a good parent is for the family to be reunited.
Obviously, take this with a grain of salt but as a victim of child abuse I felt the need to give my opinion. I truly hope it gets better for you and your kids.