I'm not sure, that kind of alienation is common in younger people in the Western world, whereas the dog mommy/daddy seems to be an English-speaking (if not American) phenomenon, and used by adults.

I am a Millennial from Europe, and I am well acquainted with the alienation of my generation, but the dog mommy thing doesn't exist in the country I'm from, and sounds something a suburban mom in her 40s would say. It makes me cringe.

I had dogs and cats growing up, and I considered my "mates" or friends rather than my children. They lived in the house, able to come and go outside, but were absolutely forbidden from sleeping on beds (except cats when the beds are empty because they don't care) or from soliciting food at the table while we were eating.