From the "Agatha Christie's Marple" TV series, I gather that Miss Marple was involved with a Captain Ainsworth. Are there any references to this also in the books? And it is suggested in "Murder at the Vicarage" that Captain Ainsworth was married. Is that correct? Are there other sources for this?
No, Captain Ainsworth only appears in the 2004 ITV series and is not a character who appears in the original books. And it is indeed implied that he was married when Miss Marple had the affair with him which explains why they never married.