Yes, keeping third parties out of the fray is just fine, even recommended. So telling your dad to not mention you is very appropriate. However, in my situation, I've found that my relatives sometimes just can't help themselves and engage with the W anyway, even if I have asked them to stay out of it. So I still DB them 'just in case'.
My thread, Carpe Diem #4 Orig Thread: Carpe Diem #1