Based on the provided reference, the answer is no, there isn't currently a trillionaire family.
Although the Al Nahyan family is mentioned, and they "tend to live like trillionaires," their net worth is approximately $35 billion. This figure, while substantial, is significantly less than $1 trillion, as explicitly stated in the reference: "I lied the Alan. Family is nowhere near $1 trillion."
Therefore, while some families possess immense wealth, none have yet reached the trillion-dollar mark.