I’m not trying to be a dick, but I think you need to do some serious soul searching, and possibly get some psychological help. First, breaking someone else’s stuff, because you don’t want to (or feel you should have to) wait your turn.
Now this dog thing? IMO, it’s selfish to say the least, narcissistic at worst. I’m no psychologist, but considering the regard you have for your pets, I wouldn’t guess you’re a narcissist.
Having a dog in the gym, even if it it’s a service animal, could become an inconvenience for other patrons. Service animal owners understand that, so their highly trained animals are generally very quiet and and low profile. Think about this, you’re working out and a dog is under foot and possibly aggressive! That’s crazy!
Plus, if the guy who just crushed another dude’s phone showed up with a dog in my gym the next week, I’d be more than a little bent out of shape. I’d let the management know it’s him or me who’s got to go.
Lastly, just like kids in a gym, it’s not safe. What if a wayward dumbbell or plate falls and lands on the dog. That would be catastrophic!
My suggestion, figure out ways to leave the dog at home with some elements of comfort, so he/she doesn’t destroy the place...and try to consider the gym a private establishment intended to allow members to escape the normally annoying shit in society.