Thank you for your question
My name is Clare
I shall do my best to help you but I need some further information first
For clarity - your mother's second husband died before she did is that correct?
How much money was involved?
Sadly what you have been told is true.
Under UK law when your mother died without leaving a Will then the first £125,000 of her cash assets would go to her husband.
Accordingly the monies in the account owned by your mother would pass to her husband on her death - and thus to his children on his death.
I am sorry, please ask if you need further details