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First of all, I'm very sorry for your loss and the situation that has transpired.
You could pursue the funeral director for breach of contract or negligence.
For breach of contract you need to show that they have failed to carry out their service with reasonable skill and care and that this has result in a loss to you.
For negligence you need to show that they breached their duty of care to you.
Both of these appear to be straightforward to prove on the facts given. However, these are the limbs to overcome if you wanted to take this matter to court.
It sounds like the directors are aware of a potential claim and are looking to settle the matter upfront. As such you should write a letter to them marked "without prejudice" offering to settle your claim for an amount you are comfortable with. The "without prejudice" aspect means that you are preserving your right to claim should they reject your offer.
In summary, it is simply a case of coming up with a figure you feel is appropriate to compensate you and putting it to them. But you should do this in a letter.
Hope this helps