Nice pictures, the affection and happiness between them is real, they look like a normal loving family to me. Max is flamboyant and over the top sometimes but when she's with her daughters she is just a proud mother focusing her attention on them, keeping the distance without steal their moment.
And that's the big difference between Mary and Max.
Max can wear all the silly outfits and be really over the top, but she doesn't view her own daughters as competition for attention. She's proud to 'show them off', while if the photo of the girls running ahead was Izzy and Josie, Mosh would be right behind trying to get in the middle of it, not standing back with a smile.
I wouldn't have liked the AAAs outfits in any other context, but for running with dogs on the beach, they're very appropriate. Agree Wax should have ditched the jacket, he looks a bit weird with it on.