David Elton, 48, had left the family's weekend home in Middleton-on-Sea, near Bognor Regis, West Sussex, without disturbing the children, driving to a beach where he drowned himself.
The former Ultramar executive director had become despondent since his company was taken over after a hostile bid, leaving him without a job but sharing an pounds 8.1m pay-off with five other executives.
Detective Superintendent Paul Westwood, of Sussex Police, said Jane Elton, 43, was found lying in a ground-floor room on Monday morning by her son Charles, seven. With him in the house was his sister Victoria, three. Charles rang a friend and asked to speak to his friend's father. He told him he could not wake his mother.
As police went to the Eltons' thatched pounds 400,000 house on the seafront, Mr Elton's body was found in shallow water on a beach at Climping by a passer-by.
Det Supt Westwood said: 'We treated this as a murder inquiry at the start, when we found Mrs Elton's body. From the inquiries that we have made, we are not looking for anyone else in connection with this incident.'
John Allen, head porter at the couple's pounds 700,000 London flat in Clarence Terrace, off Regent's Park, said Mrs Elton had asked her husband for a separation. 'I think it really knocked him back . . . he was finding that very difficult to accept on top of everything else. It was like the last straw.'
The Ultramar takeover by Lasmo North Sea was embroiled in controversy when it was revealed Ultramar directors had been paying themselves large amounts through tax havens such as Liberia and Panama. Three directors, but not Mr Elton, resigned.
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