I know you haven't mentioned the ages of the children other than to say 'very young' and so it's difficult to be prescriptive but never underestimate the strength and resilience of young children; they simply move on and process in their own way. The time will come to tell them but it will probably never seem right as they will have moved on and adjusted to life without their father. Your daughter is very definitely old enough to know the truth and deal with whatever story your wife's family decide to put out. Yes, she'll be upset but will build confidence and character in the long-term.
From my own perspective, my mother's death had some positive sides, however difficult these are to come to terms with: I became incredibly responsible and independent at a young age, able to cook for my family from around 10 years old, I was able to use a washing machine and dryer from a similar age.
I don't need to say this but support your wife hugely as she will be massively affected however brave a face she puts on and strong a personality she has.