In short, Rae, a possessive is already a mark of possession in itself, so you won't add a genitive (meaning a possession).
Imagine that " 's " is the genitive, and "your" is the possessive pronoun.
If you add a genitive in the possessive pronoun, it would make something like "my's daughter is rich", or my daughter's is rich".
You do not need to add a genitive if you have the possessive pronoun.
To express possession and similar ideas the possessive pronouns are regularly used, not the genitive (...)
[Not domus meī]
(Very rare exceptions exist to this rule, depending of the authors)
Differences between the possessive (pronouns) and the genitive (case) use, are the same than:
"my cat" and "Martin's hat."
To recognize genitive, you would have the relationship "the hat of Martin" = genitive.
Use "of" to know when you can use it.
The genitive links the name of the person/the description of the person + 's + the object owned.
It shows a relationship person/object.
The possessive addresses directly a pronoun, and show the possession for this pronoun.
The person is not named, it is replaced by a pronoun.
She has a cat: her cat.
Note: Sometimes, in this couse, we meet some special sentence structure requiring a possessive pronoun, not in the nominative, but in the dative case (=is a possession....to me, to you..),
like: nomen mihi.
The genitive of the pronoun tū is tuī, but from what I understand, the possessive adjective is preferred when specifying possession.
While tuae could be used as the feminine genitive singular of the possessive 2nd person singular adjective, it would need to modify a noun (could be implied). It would make the most sense to then assume that it modifies filiae, but that makes an odd sentence.
If we treated filiae tuae as genitive the sentence would be something like "Of your daughter, they live in Rome". Unless this is some construction that I am forgetting.
I am probably not going to be able to explain the distinction well (maybe someone else will be able to). I will give some links that may provide something that may help (whether they are the best sources is debatable).