It works both ways, with or without "az". I don't know, it may be a special case for relatives. Or "anyátok" is treated like a proper noun. Something like that.
"Anyátok" here could be rude, why not have "édesanyátok" or "anyukátok" instead?
First we learn those forms are possible:
a ti autótok
a nektek az autótok
And now, with family, a proper form is even rude???
But "a barátnőd" is not rude?