I'm wondering this too, however I'm starting to get the impression that dine is for plural words, and din/dit are singular. Din is for -n words and dit is for -t words. (Or so I've read, I'm learning just as much as you are :p)
No. in this case yours is either translated to "din" (you are talking to one person) eller "jeres" (you are talking to more than one person) . If there were more than one dog, then "din" would become "dine".