The person responsible for the Estate is not the "next of kin" ...
... a legal "non term" which carries as little significance as "common law wife".
So it matters not one jot whom the Uncle "nominated".
The Estate is handled by the person who would, under the Intestacy laws, be the primary residuary beneficiary.
If there is no spouse, or children (step children don't count) or parents, then any surviving siblings are next in line.
I stopped practising Law years ago, but trust me ... the term "next of kin" has no legal significance.
But ... the Coroner is correct to the extent that, from the sound of it, the Father is the person primarily entitled to a Grant of Personal Representation, and therefore responsible for the Estate ...
... unless he renounces his entitlement ... which he can only do if he has not "intermeddled" (ie handled any Estate assets).