Female cats are like that. When I met my boyfriend I had two female cats and the first time he stayed over at my place, they were the two biggest harlots, basically pissing all over girl code and hanging on him like he was a tall glass of water in a desert. Even meowing loudly whenever he went to the bathroom. Zero loyalty.
And then a few years ago my in-laws got a female cat and she is all over my father in law like he's made of sunshine. :b

The joke could also be on the wife depending on the perspective. Kinda in the Mrs Hyacinth kind of way. We don't laugh at Richard for being oppressed and abused by his wife. We laugh at her for being such an insufferable dummy. That's the type of joke I got out of this birthday picture. A Mrs Hyacinth joke.
Honestly, I don't think it is that deep. I think you're hurting, which is valid, but you're projecting your own hurt onto one photo and judging an entire relationship based off of one joke-pic. If we knew more about their relationship dynamic and what they are like as people, we may be better equipped to judge whether or not this joke is made by two people who thinks it's funny or made by one party to humiliate the other. We literally don't know.