Mickey Rourke was absolutely impressive with his performance in The Wrestler, which would explain why he got an Oscar nomination for the role. He's been a certified badass for quite some time now.
Look at that man. In all of his badass glory. If you don't think he's a badass, I've got 2 words for ya — you're wrong. Sure, it might be ridiculous to see such a gruff and gravely-voiced man walking around with a tiny cute dog in his arms, but need I remind you that Rourke is actually an accomplished boxer? The dude is 27-3 in amateur boxing.
So yea, that dude's allowed to walk around with a fuckin' man purse and a Pomeranian, okay? He's allowed to do just about whatever he wants. His certified badass badge has been in effect since the 80's. Don't fuck with Mickey Rourke.