I dont think that Shy's DP is her children's natural father though is he? I think she said she'd been with him for 3 years and her DCs were 11 and 9. That said, at those ages he's still been around for a significant part of their lives and is bound to be important to them. For how long out of those 3 years has he been living with you as a family Shy?
It is hard to know what to do for the best as far as your DCs are concerned. What was their relationship like with him Shy?
Although this is tough on you all at the moment, one thing you can focus on (and I know it's a hackneyed old cliche) is that children are incredibly resilliant and they have an ability to bounce back if other aspects of thier lives remain stable and constant - i.e they keep up their usual routines with school, friends, other family members, hobbies/activities etc and of course you are the one constant factor in their lives - their anchor and the one they look to. They wil draw comfort and security from the things that are familiar to them.
Whatever shit is going on around them it is importnant to maintain a degree of tactful honestly with them too but at the same time shielding them from it as far as is practical and possible.
In your shoes, I think I would be tempted to tell them that there was a lot that went on between you two as grown ups that they as children could not, or would not, be expected to understand at their ages. Say that the reason that things didn't maybe appear to be so bad to them was because you both tried your very best to make sure that they didn't see arguing because neither of you wanted them to be upset or worried. Maybe you could find a book in the library that might help you tackle the issues that might arise from the separation from the children's point of view sensitively? There are lots of books aimed at children that deal with all sorts of "issues" that affect them. Just a thought...
I think the main problem you have here really is them possibily still wanting to see your DP. Had he been their natural father the issue of access would have been far more cut and dried but here, with abuse being an issue, I think that there is a very real possibility that your he could use the children as a way back to you. Obviously that's something you need to be alive to.
At the moment you are a bit like a drug addict going cold turkey and it's to be expected that you are having very, very bad days. It is early days and you shouldn't feel despondent. Broaching the subject with the children is bound to make it all seem worse too because you're now having to deal with their upset as well as your own too. I can see that might bring feelings of guilt on your part too, which are more understandable because you introduced him into thier lives.
It may not feel like it but you have come a long way already and you should be very proud of yourself.
Try and remain positive and focus on better times ahead in the future, rather than dwelling on the past. If you must dwell in the past try and balance your tendancy to dwell only on the good times with remembering the bad times too - the times he "stonewalled" your DC when in a mood and didn't let you visit your parents and all the nasty, hurtful things he said to you.
Your DCs will I'm sure bounce back from this with the right support from you and others close to them.
With the right support you will all make it out of this and move on to better things.