Doors and windows

For me, there are two reasons to learn a language. There's the motive of deepening one's enjoyment of a movie or understanding the original version of a favorite book, and there's the motive of being able to say, "move your cart, buddy - you're not the only one in the aisle." Been reviewing this movie based on an old play - garishly colorful and in Mandarin and with captions. (Nobody minds if I use a language I wasn't born to, do they? Rhetorical.) There's one detail that bothered me, and also might fit my current situation (possible [definite] mangled romanization ahead) - if it's "wo bu shi ni muhou" for "I am not your mother," yet it's "ta shi ni de gugu" for "he is your brother," why is "de" used in the second sentence?
Is it because one is first person to second? Is it because the other is affirmative rather than negative? Could I use either of these, "your brother" and "your mother," in the same way I'd use "your cart" in English - would there be a difference between speaking about animate versus inanimate objects? And of course, none of these questions address the tone detail. Meh. The internet is large enough that I'll find my answers - within a couple of weeks, as it happens. (Addendum - got my book earlier than expected, so thanks much.) If the trouble with learning revolves around internet access, there are ways to get online at so many places nowadays - local libraries, coffee shops (two fixes, one trip), internet cafes, et cetera. Took a look at California's library system - at least one county's libraries allow one free computer session daily to its cardholders or to those with a pass. (Cards and passes can be obtained with a valid state-issued ID, if I remember correctly. If you're without one, that's beyond my scope.) Coffee shops might require a purchase - fair enough. Internet cafes might have minimums (say, two hours at $5.00 depending on the time of day) that don't include headsets within the fee. Reality - access to the internet, and therefore to learning, is nearly ubiquitous, at least in the States. Can't access education one way? Find another way to learn.