In the case of Coles v Reynolds & Anor  EWHC 2151 (Ch), whilst it was accepted that the deceased had been persuaded by one of the defendants in deciding whom to benefit under her will, the Court rejected the claimant's allegation of undue influence.
This case therefore reaffirms the fundamental principle that persuasion does not amount to undue influence. The party asserting testamentary undue influence must convince the Court that there has been coercion, i.e. pressure that overpowers the testator's volition, such that the testator is not exercising their free will.
The heavy evidential burden under which claimants alleging testamentary undue influence find themselves explains the scarcity of successful claims in this area. This has led to calls for reform and the possible introduction of a presumption in order to bring testamentary undue influence more in line with its inter vivos counterpart. For a more detailed discussion of these issues and the recent case law, please see this firm's article that was published in the September 2019 edition of the Trusts and Estates Law & Tax Journal (https://www.forsters.co.uk/news/opinions/emily-exton-rebecca-welman-write-undue-influence-trusts-estates-law-taxjournal).
I agree that the first defendant persuaded the deceased not to make pecuniary legacies to her grandchildren, despite her wish (provisionally expressed in the absence of the first defendant) to do so; but persuasion is not undue influence;