I have been googling, and found the following information, the basics of which I have written. But please read the information in full.
www.advicenow.org.uk/data/files/lt-wills-2010-72.pdf
As executor, not only is it up to you to deal with this, but you are responsible for what happens to the children's share until they are 18. Were you aware of this?
Because they weren't married, you and the other executor need to be dealing with all of this.. And even if there was no will, like she tried to claim and told a load of bollocks about, she still would not be able to take over. Sorting everything out without a will, would either be the state or his family. If he was married to your friend, it would be her. If not his parents, siblings, uncles, cousins, depending on who is alive in his family.
As executor, it is also down to you to sort out the funeral.
Have you applied for probate yet? You need to jump on this, without this you cannot deal with the estate. So this asks the question of how the hell is she doing any of this. Or you can instruct a lawyer to do this, and the money comes out of the estate... Anyway, once a million bits of paper work have been done, you get a bit of paper called grant of probate.. This shows all the companies, you are dealing with everything. Once you have gained every single penny that he owns, you pay off any debts. Then the rest gets distributed according to the will. You cannot do as she is suggesting, because the legal heirs to the will can come back and sue your arse off. If you don't pay the debts from the estate, creditors will come after you.
The will can be changed by negotiation and agreement. Threatening, and being a nasty, grabby, bullying bitch does not come under this. Because the children are under 18, you cannot do this either. It can only be changed by court...
Now, how long was she living with him? This could be where she is getting confused. If over 2 years, or relying partially or fully on him, she could be able to make a claim. But how she is doing it is wrong. This falls under Provisions for Family and Dependence Act 1975. However, she has to write her request stating why. She has to take legal advice and she has to pay for this.