Well, that's certainly a "Mrs". The second initial could well be an "E". The owner surely must be Katie Elizabeth Brewer nee Woods.
The date could certainly be when she acquired the card. If that style of uniform was not still in use in 1934 then the picture must have been taken earlier.
If it's not her husband and family then the only other possibility that occurs to me is Ernest James Woods and his family. He appears to have married in 1907, to either Mary Gilbert or Grace Johnstone, but I've no idea if he had any children.
David