"However who would be in charge of looking after the money in trust for the children? Would it be the woman or the man’s mother who is in her 70s?"
There is a specific order as to who can apply to be the administrator of an intestate estate. This is set out by Rule 22 of the The Non-Contentious Probate Rules 1987.
https://www.thegazette.co.uk/all-notices/content/104036
The list is:
- Spouse of civil partner
- Children of the deceased, which also includes adopted children and those born outside of marriage.
- Parents of the deceased
- Full siblings who share the same parents (or their children)
- Half siblings who share one parent (or their children)
- Grandparents
- Full aunts or uncles (or their children)
- Half aunts or uncles (or their children)
So, it is the children that can apply to be the administrator of the estate before the parents can.
However, in the case the children are under 18. So what happens then?
Well, in the event of minor children, who, but for their age, would be entitled to act, then the person with parental responsibility for the minor(s) would be entitled to take out the grant of administration on their behalf.
This comes from Rule 32 of the Non-Contentious Probate Rules.
In addition, the person with parental responsibility may also nominate a second person to act with them as well (as long as the other person is a "fit and proper person").
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So, to sum things up, the children (or just one of them) is the person who is entitled to apply to administer the estate.
However, since they are under 18, then the person with parental responsibility can apply on their behalf to administer the estate for their benefit until they reach the age of 18.
"However who would be in charge of looking after the money in trust for the children? Would it be the woman or the man’s mother who is in her 70s?"
It would be the woman. Unless she chose not to act, in which case it would then be down to the mother as she is next on the list after the children.