"Your mother has a restaurant."
Translation:Din mor har en restaurang.
You can say er mor if you're speaking to two or more siblings who have the same mother. Some native speakers also use ni as a 'polite' pronoun, whereas many others don't like this, native speakers disagree among themselves about this as you can see here: https://www.duolingo.com/comment/5591933 (for one thing, ni is used more often this way in Finland than in Sweden).
Sin is for things belonging to the object of the sentence. I think of it as "their own". Din is "Your".
"Adam tar din tallrik"= Adam takes your plate
"Adam tar sin tallrik"= Adam takes his own plate
"Adam tar hans tallrik"= Adam takes his plate [Where "He" is someone other than Adam]
One owner, one possession- din or dit (Din hund, ditt barn)
Plural owners, one possession- er or ert (Er hund, ert barn)
One owner, plural possessions- dina (Dina hundar, dina barnen)
Plural owners, plural possesions- era (Era hundar, era barnen)
Er also turns up as the plural of dig (or object form of ni, if you prefer). this can be tricky because English just uses "you" for all these forms, so hopefully someone will correct me if I get it wrong:
I give it to you, you give it to me= Jag ger det till dig, du ger det till mig
We give it to you, you give it to us= Vi ger det till er, ni ger det till oss