The funeral grant looks attractive. Correct that if the deceased owned a house which is left to a widow it does not have to be repaid. However, she is not the widow. She is a divorced spouse.
Let's assume he dies, ex-wife arranges funeral with local funeral director. Incurs costs of £3,000. After some time, funeral director gets fed up of waiting for his money and sues the widow. (Whilst the estate is primarily responsible for the funeral costs, if there is no estate (and there is here), the widow will have to pay if she incurred the debt). Result could be a Court case, a CCJ and then potentially a charging order. This *could* result in the sale of the house, but the Court may well take a view on the proportionality - particularly in light of the disabled son.
This needs thinking about now.
One way of avoiding it is to consider the house being transferred into a trust. This could be done relatively simply and at not too much cost (probably £200 - £300 - and you might get a solicitor (or counsel) to accept payments by installment. The trust would need to have some thought put into it as to how it would work (there isnt enough info here) but if the house is owned by the trust then there is no estate on death.
Then the son applies for a funeral grant (he will fit the definition of close relative).
If that is too complicated, I would suggest that the son coughs up the money for the funeral. Very often funeral directors will accept payments by installments.