I found the order of these sentences amusing and especially useful if ever I were a man in Sweden being picked up by a woman or if I were single in Sweden.
The previous sentence to this one was " Kommer du ofta hit?" Thanks for upping the dating game, Duo!
"I have a wife already" or "I already have a wife" should both work for this. The "I have already" structure works when followed by a verb (I have already done that) but sounds very unnatural when followed by a noun, or at least that's the case where I'm from (Midwest America)