I think the translation would become "I was always using dad's car", but the sentence is "I always used dad's car", which to me implies that I no longer use dad's car, in which case the preterite is correct.
If you intend to make an accurate translation, NO.
"Dad" is "papá", "daddy" is "papito" and "father" is "padre".
So "I always used father's car" would be (in a very old fashioned Spanish because nowadays almost no one refers to his father like that) would be "Siempre usé el coche de padre"
Let me remember also that "CARRO" is only used in Southamerica for "CAR". In Spain a "carro" is used for "CART" like in "A horse cart". We in spain say "auto" or "coche".
Are you claiming father and papa don't mean the same thing? You are making up these direct translations. "papa" and "padre" both mean ones father despite the way you feel they should be translated.
In Spanish ALL the information is INSIDE the verb. (Person, number and tense). Not as easy to remember as English tenses, but richer and more plastic to build sentences. Also sometimes in some cases it leads to confusion.
usé is the first person singular preterite (past tense) conjugation of the verb usar - to use. there are good references for conjugating the -ar, -er & -ir regular verbs online. just google Spanish verb conjugations.