Translation:Žofie can't stand her cousin Kateřina.
I'm not fluent in this language but I think it works like that because it means that in this case it is their own cousin (and not some other person's cousin). So in this case it is Zofie's cousin as in Zofie can't stand her (own) cousin. Or in the case of Mám svou ženu you'd translate it something like "I have my (own) wife." Hope this makes any sense and if it doesn't, I hope someone does better job explaining it :)
I would say that doesn't work here. The only examples that immediately come to mind would be along the lines of "I can't take it anymore" or "I can't take ibuprofen because it upsets my stomach" or "I can't take you to school on Monday." To my (native AmE ear, "Zofie can't take Kateřina" as a stand-alone sentence sounds weird. It begs the question, "You can't take her where?" as in my third example.