Thinking back to when I was at school, a "cool mum" to me, would have been someone who looked young, dressed well, bought their kids amazing clothes/school bags/stationary, made amazing unique packed lunches, took their family on cool trips in the school holidays AND MOST IMPORTANTLY not doing or saying anything cringey or embarrassing publicly...
When I was 11, if I heard of someone's parent with bags galore around their eyes to the point they looked like they were coming up 50 rather than their actual age of 30, wearing the same smelly stained hoody day in day out, dressing their kids in literal non branded rags that are about 4 sizes too big, only taking them away to places where they have nothing to do but pick up stones on the beach in silence while mama gets her tits out and their dad ogles the "bacon", feeding the kid a diet of greige slop with no branded items or treats, being on porn hub, not even for being sexy, but cos her fanny was massive and fat, and to top it off dancing about the house with all the moves of a 75 yo uncle at a wedding after a few too many sherries, making the kids join in and then posting it to the internet, then i can guarantee you the other kids would have thought that was the direct opposite of "cool mum vibes 4eva" they'd have thought that it was incredibly weird and the piss would have been ripped out of the poor kid belonging to such a family