OP, please don't think that you don't have any further recourse; if this is a payout from an employer's pension scheme, there will be a disputes process where you can challenge the decision. It's possible that the trustees made the decision based on incomplete or incorrect information (so, the new g/f represented herself as financially dependant). It's also entirely possible that she shouldn't have been considered as a beneficiary at all - most pension scheme rules are very wide, and would include those who are financially dependent, but not all include financial co-dependency. Financial dependency means exactly what it says on the tin - g/f would have needed to have been completely reliant on your friend to provide her with all of the "ordinary necessities of life", so food, shelter, clothing, bills. Financial co-dependency is much wider, but just sharing a house/joint bank account might or might not cut it.
I agree that the trustees may have been taking the view that the children would have been adequately supported with a quarter of the total amount; however, it's likely that they reached that conclusion on the basis of information given by the g/f, which they didn't challenge. They had a duty to make proper enquiries, and it doesn't look as though they did that.
Also, although a death in service benefit can be a huge amount of money, in practice the discretion to distribute it might well be delegated to an administrator, rather than being considered by the full trustee board. The speed of the decision suggests this might have happened here. Delegation is fine where the situation is uncomplicated and the trustees just want the widow and children to have the money quickly. This doesn't sound like an uncomplicated situation.
I can't give you advice on this, because I don't have the full picture; I know what you've said on the thread, but I (and you) don't know what the g/f has told the trustees. There is a charity called TPAS (the Pensions Advisory Service) who help with disputes, and who can make further investigations, and support you if you want to appeal to the Pensions Ombudsman (which is free). Don't know how to do links, but they're easily googleable.
And I'm very sorry for the loss of your friend. He sounds like one of the good guys.