Bednobs,
Even though the children's mother is still alive, but divorced from the deceased, that's that, and the children become the next of kin, and will receive the estate under the intestacy rules. Anyone can register a death, and arrange for a funeral, for example, if the ex-husband hadn't remarried, but had a live-in partner, then that partner could make all the foregoing arrangements, but would not have any entitlement to his estate. But it would be hoped, that in these kind of circumstances, funeral arrangements would be discussed with the ex-wife on behalf of the children.