"I want to have a family."
Translation:Chcę mieć rodzinę.
Generally, chcieć doesn't require a reflexive pronoun, the verb works just as in English.
Technically, you can add się to almost any third person singular conjugation of a verb to make a impersonal statement:
Tak to jest, gdy się chce być artystą. = That's how it is, when one wants to be an artist (more commonly: when you want to be an artist).
Then, there is also the dative construction "Chce mi/ci/mu/nam... się". It's hard to explain the difference, but it seems like chce mi się refers to a more spontaneous and temporary wish than just chcę. The closest English equivalent would perhaps be "I feel like doing X".
chcę się doesn't work in any context.