Henpecked? Old Folk Art Sculptures of a Family

I was surprised to see the phrase "henpecked" shown in online dictionaries without calling it outdated and offensive slang.  Most words describing women as animals seem sexist to me,  especially "cougar" which is the name of a dating site.  Still with father here clenching his throat and the women in his life twice his size, they might be capable of ganging up on him a bit.  Tallest female is 18 inches while dad is half that.  He isn't "tied to her apron strings" which is another phrase drifting away, I think...but we also have an apron here.  "Led by the nose" hardly applies, as Dad's nose is flat as a piece of plywood. 

Folk Art Family in Original Paint circa 1940 Collection Jim Linderman