The contract of insurance was between the mother and the insurance company. The mother's death automatically cancels that contract. The insurer should be advised of the death and a refund of the unused part of the premium sought. (The insurer will probably pay that to directly to the widower, but it might be necessary to wait until probate has been obtained).
If the widower plans to become the main driver of the car, he should seek a new policy with ANY insurer (not necessarily with the old one), adding his daughter on as a 'named driver'. If the daughter is to become the main driver of the vehicle, she should also seek a new policy in her own name (again, with ANY company).
There should be no reason for any delay in obtaining new insurance cover. It can be obtained instantly, either online or by phone. The name of the registered keeper is not relevant but it would make sense for either the widower or the daughter (whoever is most likely to drive the car) to get the vehicle transferred into their name. (The legal owner of the car will be the widower, unless he chooses to give it to his daughter, But there's no reason why the legal owner and the registered keeper should be the same. Millions of company car drivers have their name recorded as the registered keeper - so that speeding tickets &c can be sent directly to them - even though they don't own the vehicles).
Allowing a bit of time to look at some of the insurance comparison websites, everything can easily be sorted out within half an hour or so, so it's hardly a major problem.
Chris.