I'm frankly still baffled most of the time as to when the definite article is required, and when it is dropped. For instance, in english, it's 'the shower'...but no definite article in the Italian.
If I remember correctly, in an earlier example, "He always cooks meat on the grill", it has to be "il carne" rather than just carne.
The one example I do understand is you can drop the def article when using the possessive when talking about close family members, e.g. "mia moglie" instead of "la mia moglie"
Just to make you happy (or confused, lol)... I'm Italian, and in a sentence like this I would never say "in doccia". I would probably say "sotto la doccia", but if I were forced to use the preposition "in", I would say "nella doccia".
Maybe I have heard the expression "in doccia", but I think it's a regionalism. I don't know what if it's really correct in Italian, but I can't exclude that the one who is wrong it's me.
I feel that, based on the context, "in casa" should be acceptable, but in at least 90% of the cases you will probably use "a casa".