It's sloppy in two respects: 1. People use "Dad" and "Mom" as names, but not generally for a brother. 2. When using "Dad" and "Mom" as proper nouns (like names), they should be capitalized.
When you are using the word "Dad" to refer to a specific person, it's standing in place of their name, and thus, like their name, would be capitalized. When you're talking about dads in general, it's a common noun. http://english.stackexchange.com/questions/44846/when-should-mom-and-dad-be-capitalized
This construction is not used only for interpersonal relationships.
It's used whenever you want to say that someone possesses something (but not sexual possession, as in English).
Russian sidesteps actual "ownership".
The way I remember it is that the construction was derived from a mentality that nobody (except the czar) really owned anything, they just had things near them.