I was thinking about this - before you show your hand to her and say that actually you have the will, do you have it in writing anywhere from her that she appointed herself executor and that there was no will made after splitting up with the ex partner, or is it all from phone conversations?
If it is just phone conversations then it might be worth your friend sending a simple email to her along the lines of 'just want to confirm our recent conversations about ex-p's estate so I can explain it to the children and make sure I have my facts correct. You believe that there is no will, that ex died intestate and you have appointed yourself executor. You are going to give yourself 2/3 of ex's estate and give his children, A & B, 1/6 of his estate each. You have contacted xx insurance company to notify them that the next of kin details should be changed to you and have informed them of the percentages due to each beneficiary'. If she knows about the other will then add a sentence along the lines of 'you believe that the will that ex made on [date] is no longer valid since he started to cohabit with you from [date] due to the new cohabitation laws.'
Wrap it up with 'please can you confirm that I have understood everything correctly? Please can you confirm the details of the solicitor dealing with this for my records. And on a personal note, with regard to the effects of my ex, I would be very grateful if you could ensure that both his children have some of his personal things to have - losing their father so young I believe that having something tangible that belonged to him will help to provide them with comfort and a sense of connection to him both now and through the years as they grow up.
Then when she replies you will have written proof that she thinks there is no will and the dodgy way she has gone about trying to screw your friend's children from their rightful inheritance. If she miraculously produces a different will further down the line, you will have good reason to challenge it if you have it in writing that she thinks he died intestate.
You also have enough to challenge the solicitor and the insurance company as they shouldn't have let her get anywhere near this far along the line if she had said he died intestate and then said she was the executor and then said about children - alarm bells should have been ringing all over the place that everything should have gone to his dc.
Just out of interest, did the ex die unexpectedly or did he have a terminal disease so knew he had to get his paperwork in order? Particularly if it was the latter, if there is no other will, that should be a good reason to argue the old one stands. And even if not, surely if you were a good enough friend to be an executor he would have told you if he ws going to change things or remove you as executor in order to prevent precisely this happening.