We had a grapevine in the back yard, and our dog snacked on the grapes that fell on the ground, until he got really sick. Of course he got sick on the weekend and we had to go to the emergency vet, so it cost an arm and a leg to bring him back from death's door. Don't let your dog eat grapes!!!
The definite article is almost always required before a possessive in Italian; the exceptions are before most close family members unmodified and singular (e.g. "mia madre", "mio fratello"), as a predicate (in which case it's optional, i.e. "è mio", "è il mio" are both correct), and a bunch of idioms (e.g. "casa mia", "a mio avviso").
"il mio cane" doesnt make sense for a native english speaker. It does make sense for a brazilian,we do the same(latin based language also);but there are a lot of things that sound weird to me in english,thats because the languages are very different. You have to adapt it to your own language whenever you translate it.