The first time a native says mia sorella, with nothing in front of it, it seems like sloppiness or a regional habit. Somebody taught you early that Italian possessives come with the article (la mia casa, il mio lavoro, la mia macchina), and that is true, and English speakers who skip the article sound wrong for years. So you kept it, and la mia sorella is the consistent sentence that follows from it.
It is neither. The article goes with every possessive except one case: a single, unmodified family member. Mia sorella, mio fratello, mia madre, mio padre, nostro zio, tua cugina. One person, one bare family word, no article. That is the entire exception, and it has three switches that turn it back off.
The switches are plural, modification, and loro. Make the family member plural and the article returns. Attach anything to the noun, an adjective or a diminutive or a phrase, and it returns. Use loro as the possessive and it never left in the first place. Everything else about possessives is unchanged, which is why this is a small rule and not a new system.
You will also want to notice, before it bites you, that “family” here means family by blood or marriage. Il mio ragazzo, my boyfriend, keeps the article, because a boyfriend is not a relative however close he is. So do il mio amico and il mio collega.
Mia sorella vive a Torino.
I miei fratelli vivono a Torino.
La mia sorellina ha sei anni.
Il mio caro padre non lo direbbe mai.
La loro madre è medico.
Read those five in order and the shape is clear. The bare form is a narrow window: one relative, one word, nothing decorating it. Widen the sentence in any direction and Italian puts the article back, because the possessive is behaving like a possessive again rather than like part of a name.
The edge that trips people up
Two cases sit outside the neat version, and one of them is very common.
Mamma and papà are the affectionate words, closer to “mum” and “dad” than to “mother” and “father”, and they are commonly heard with the article: la mia mamma, il mio papà. You will hear both forms, though. Mia mamma è in cucina and la mia mamma è in cucina are both ordinary sentences, and neither one will be corrected. Here you can stop worrying about which you picked.
Loro is the other edge, and it is absolute. Where every other possessive has the family exception, loro has none: la loro madre, il loro fratello, i loro figli, always with the article. Loro also never changes shape (no lora, no lori), so the article in front of it is the only thing carrying gender and number, which may be why the language refuses to drop it.
It helps to be clear about what the rule is not about. It is a rule about possessives, and only about possessives. Una sorella, questa sorella, la sorella di Marco all behave the way you would expect, because no mio or tuo is involved. Nothing about family words themselves resists the article.
A few more family sentences to fix the boundary. Mio zio abita a Napoli: one relative, bare. I miei zii abitano a Napoli: two, so the article. Mia sorella maggiore studia a Pisa, and here both forms are said: mia sorella maggiore and la mia sorella maggiore are each ordinary, and you will hear both. Maggiore and minore are the clearest case of an adjective that does not reliably bring the article back, because they work as part of the family word rather than as a description of the person, and gemello behaves the same way in mio fratello gemello. So read “attach an adjective and the article returns” as the rule for every other adjective, caro and piccolo and the rest, with this small group as the exception inside the exception. And i miei, on its own, means my parents, which is a small gift of a phrase: stasera ceno dai miei, tonight I am eating at my parents’ place.
How to hear it
Count, then look. One plain family word after mio, tuo, suo, nostro or vostro, with nothing attached to it, means no article. Anything else (plural, almost any adjective, diminutive, loro) and the article is there.
The useful thing about this rule is that it fires early. The article, if there is one, is the first word out of your mouth, and by then you already know whether you are about to say sorella or sorellina, one brother or two. You are not repairing an ending halfway through a sentence, the way you do with agreement. You are choosing a word before you start.
The absence is the interesting part of this one. With a single plain relative, Italian treats the word almost as a name: mia madre needs nothing in front of it, the way Maria does not. Start describing the person instead of simply naming her, dear or little or one of several, and she becomes an ordinary noun again, and the article arrives with the description. That is roughly what la mia sorella has always sounded like to an Italian ear: a label pinned to someone who already had a name.