"At my house it does not happen."
Translation:A casa mia non succede.
Putting the possessive after the noun is pretty common in Southern Italian dialects, and it isn't bad grammar in proper Italian either, just uncommon. The case with casa is special though, as "la mia casa" is "my house", while "casa mia" (no article!) is "my home". The case with "a casa mia" is even more special, and the given "at my house" doesn't really capture the nuance: it's often a colloquial way of saying "where I come from", "what I'm used to", "in my experience", "in my opinion". So "a casa mia non succede" could be taken to mean "I'm not used to it happening", "I've never seen it happen", "it would be odd for it to happen".
Now, given that the exercise was from English to Italian, your translation "alla mia casa" is probably closer to the original :)