Ida

Yeah, that's the transgender subtext.

There is no evidence as far as I could dig up that the actual Ida Kitaeva Raphael Laurel (1899-1980) was anything other than a cisgender woman. As for the movie, it appears it was a joke, one that he started playing a few moments before, when he daintily puckered up and stayed still with his eyes closed, prompting Ida to lean over and kiss him, drawing her into reversing a typical gender script (where men were expected to do the lean-in for a lip-on-lip kiss). He got the idea to joke about gender roles because at the beginning of the conversation, Ida speculated of Lucille "I think she wear pants in Hardy house, no?" yet by the end of the exchange Ida herself strictly instructed Stan not to drink and grabbed his glass and drank it herself.

Lest there be any confusion, the "Raphael" in her name prior to marrying Stan was taken from the name of her first husband (who passed away in 1942) the concertina player Raphael Alexandrovitch Sonnesburg, who went by the stage name of simply "Raphael".

On the DVD extras they say that the actors who played the two wives ad libbed a lot of funny lines. Perhaps this was one of them.

Are you allowed out alone?

I was scratching my head over that one too, wtf..? I know we are know living in the age of any gender or non gender is possible but in the 1950s..? :D