Keith Hall, 38, clung to the couple's two young sons and spoke about their life without his wife Patricia, 39.
Mr Hall, a mobile grocer, was speaking for the first time since a jury at Leeds Crown Court found him not guilty of the murder or manslaughter of his wife.
The trial judge ruled a taped confession he allegedly made to an undercover policewoman to be inadmissible as evidence.
Mrs Hall, a part-time cosmetics sales representative, vanished from their home in Pudsey, near Leeds, West Yorkshire, over two years ago after a row.
She has not been seen since but police decided to bring a prosecution against Mr Hall, even though there was no body, after the taped confession.
He allegedly told the undercover officer, known only as Liz, that he had strangled his wife and burnt her body in an incinerator. But Mr Justice Waterhouse decided the confession was unreliable and breached rules governing the questioning of individuals.
Yesterday he returned to the house he shared with Mrs Hall. He hugged their two sons, Andrew, 11, and Graeme, 7, and said: 'Today is a difficult day for them without their mother here.
'Andrew, in particular, is old enough to understand that she isn't here. They miss her terribly but they don't say a lot about her.
'They tend to keep their feelings bottled up. I've tried to explain things to them but it's not easy.
'It's the kids who have kept me going through all this. It has been an ordeal for me but they have kept me strong. Now I have to keep that way for their sakes. They are all I have got to live for.'
On the mantelpiece in the lounge was the card he had bought for Mrs Hall. It read: 'To my wonderful wife, with love on Mother's Day.' Inside he had penned a personal message to his missing wife.
He said: 'I still believe Pat is alive somewhere and I still carry the hope that one day I and the kids will have her back again.'
Mr Hall rejected claims that he had tried to cash in on family tragedy by selling his story to a Sunday newspaper. 'I did not approach them. It was the other way round,' he maintained.
He said he had lost his business and would need to claim state benefits, adding: 'I have to think of the kids now. In the world today you need money to live . . . That's a fact of life.'
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