What you need to do is look at it from a completely different perspective.
He was abusive, he called your disgusting names, you got rid!
Now someone else has got him and good luck to her! She's having to put up with him now, not you. You are FREE! Just keep telling yourself that - FREE, FREE, FREE .... whereas she is now lumbered with him.
He's the same person. He's not going to change miraculously overnight into the perfect partner. Sooner or later (if it hasn't happened already) she'll do something 'wrong' and she'll be on the receiving end of his abuse. Leopards don't change their spots - they just don't. It's early days still for them, and you can bet your life savings, it isn't all wine and roses, no matter what front they may put on.
I'm not sure why you're angry - you split and how he's with her. So what if she was 'a friend' - she's not anymore and neither is he and sounds like you are well rid of both. He's your abusive foul mouthed STBXH and you quite rightly got rid of him. Now he's her problem, not yours, and she is his. I'd be cheering from the roof tops if it was me.
Time passes, kids grow up, everything changes and one day your kids make decisions for themselves and make up their own minds about things. But right now, the deal is the kids go off to their dad's, and while they are there they are his responsibility. By stewing and seething while they are there and thinking 'it's not fair' ... the only person you are hurting is yourself. Your thoughts are hurting you - no-one else - not her, not him, not your kids .... none of them are bothered. No-one is doing anything to you - you are doing it to yourself by seeing things from your current attitude and perspective.
Try looking at it a different way entirely. You split up - tick. He's got a new partner - tick. Your kids go to theirs - tick. That's how it is. It's the same for millions of people the world over when marriages/relationships break down. There's absolutely no point in making yourself so unhappy over it - fuck him, fuck her - you've got good supportive RL friends you say, you don't have to put up with his abusive shit anymore, you are getting some child free time while he has the kids - so please don't waste it being unhappy and angry!
Use it for you. Go out, have fun, see friends, pamper yourself, go for a hike, go see a film, read a book, have a facial, meet a friend for dinner ... do things for you ... and just enjoy the freedom you have gained for yourself by getting free of of this nasty abusive man.
And as for the whole dating thing - if you don't want to do it, don't do it. Just because your ex is in a new relationship doesn't mean you have to be. Take some time out for YOU for a while. Relationships are not the be all and end all, and we don't need to define ourselves by them. There are thousands and thousands of women who are quite happily being single. I'm one of them, and there's plenty more here on MN. Focus on yourself for a bit and fuck the ex and his partner. They are not your problem and certainly not worth you making yourself unhappy over.
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