"Corro a casa tua."
'Corro alla tua casa' is a possible translation i think, but it means something slightly different. Italians use 'casa mia' because it means my home, or the place where i live, in an affectionate way. 'La mia casa' means my house, but it's just a house and not a house i have a bond with. La mia casa is something you'd hear a real-estate agent say if he talks about one of the houses he is selling.