I'm normally a low-key, easy- going person who gets along with everyone.  It was a life surprise to realize I had such a deep, emotional hatred toward BM.  Like you, I was experiencing a lot of negativity from her and she seriously affected my relationships with the SKs in a bad way.  I was also jealous of her, I think I was jealous of the years she had had with DH and her parent bond with him.

Now that 40+  years have gone by and now that she is gone, I regret the brainspace I gave her.  I have also learned that she was jealous of me, too.

I don't know the answer for you, it is so deep and painful.  When I was in counseling, as I started to ruminate on, "she did this" or " she said that", my counselor would redirect me to the present.

Good luck, it's hard.

The BM in my life is a complete waste of space. She abused DH for years and continues to do so. She plays the victim at every turn and has convinced others - including DH's dumb, dumb of a brother and narcissistic mother - that DH and I are just out to get her. She is a liar who regularly engages in fraud and seems to manage to get ahead because of it. She has also brainwashed one SS into thinking DH is a terrible person and he (SS) is "old enough" (his words at age 14) to "know the truth". 

Everything about BM flies in the face of my values. It also highlights that people who lie, cheat, and steal (in her case, literally for all three) do get ahead, which seems so unfair.

The only thing that has helped me get over my white hot rage at her is to completely cut her out of my life and pretend that she doesn't exist. This is easier to do now that SSs are in high school. MIL has gotten all in a snit that I ignore BM, but I don't care. I don't care about BIL, either. They don't know what she's really like and they don't care that she continues to abuse DH and is not above pulling her children into the drama, so their opinions don't matter to me. I've have to accept that BM will always end up looking like the martyr / victim (due primarily due to societal conventions and her ability to lie with a straight face), but that doesn't mean I have to make space for her in my life. I've created a space for her children in my life and provide for them when they are with me, that has to be enough for everyone involved, because that's all I'm giving.

It's normal to have these feelings towards someone who behaves in such a very hostile manner towards you.   And I hate to say it, but if she speaks in a very negative way to her children about you - then it is probably only a matter of time before your relationship with them becomes difficult too.  I had this - the NPD BM in my life talked about me in a horrible way to the SDs before she'd ever clapped eyes on me.   Don't beat yourself up about your thoughts about her.  The one piece of advice I would give you is try to take the long view.  Now that my SDs are in their 20s, their mother has become an irrelevance in my life.  I would love to know how your DH is able to be so cool about it all?  Maybe you are carrying all his anger as well as your own. 

I'm typically not an angry person myself. Like true angry, not like miffed bit, is rare for me. 
 

I have found that often, when I am absurdly angry, and I can't let it go-it's because I'm hurt. Should we give a damn about BM liking us, seeing the work we put in of behalf of her kids, should we feel the need to be validated as a good human? F no. But often times we do. Because we are good people. And trying to please the unpleaseable hurts. But anger feels stronger than admitting you're seeking the validation of a human would could not be more suited to withhold it from you. 
 

I offen find recognizing that, assist greatly in letting it go. 

I'm typically not an angry person myself. Like true angry, not like miffed bit, is rare for me. 
 

I have found that often, when I am absurdly angry, and I can't let it go-it's because I'm hurt. Should we give a damn about BM liking us, seeing the work we put in of behalf of her kids, should we feel the need to be validated as a good human? F no. But often times we do. Because we are good people. And trying to please the unpleaseable hurts. But anger feels stronger than admitting you're seeking the validation of a human that could not be more suited to withhold it from you is neither easy nor palpable.  
 

I offen find recognizing that, assist greatly in letting it go. 

My healing started when I decided BM was dead to me.

I didnt realize this in the white-hot heat of the moment but I've come to realize that BM was a factor in creating the man I fell in love with.  I think she "smoothed off some of the rough edges"  I don't think I would have been attracted to his younger, wilder self.  Plus, I had 2 kids and he was an experienced father.  There is something (positive) to be said for a man who has been married and has had children, believe it or not.  Lol.

No matter how awesome you are, there are some people in the world that still won't like you.  You can't base your self-worth on that, it's all about them and not about you.  Don't take it personally.

Living in a foregin country, you must be lonely, and I hope you make some friends and fill your life with joy.  Forget BM.  Avoid her at all costs.  Either don't do the exchanges, or let the kids walk themselves to the door without you.

I can still get more worked up than DH about his ex. I think in  part it's being on the outside of it and able to see how twisted their dynamic is, and he's so used to it, he's immune to it all. My HCBM is the opposite: she's tried to befriend me and sends me texts she asks me not to tell DH about and messages to me through the kids and all sorts of screwed up stuff. So I don't have to deal with her being cold or dismissive to me, but her warmth is also diabolical. I just keep a super big wall up there and don't do any parental duties and have almost no contact with her. Still get mad sometimes by ways she warps the kids and messes with DH, and maybe there's no letting it go entirely, but yeah, if you can minimize contact I find that these BM's take up less rent-free space in your head.

Sounds like the BM you are dealing with is extremely similar to BM2 .

I felt like this about BM2 too mostly because of the way she treated DH. 
The good news. Since the skids are now adults I have not run into her in years. 
BM1 and DH's childhood sweetheart I will happily sit and chat too no issues there .