As I understand it, the full frame will give more DOF at the same distance. However, the inverse is true if you're framing your subject the same way as the crop would require more distance.
Honestly, in this regard I'm lost. I suppose if you frame the shot the same way, then you would be further from your subject, affecting the depth of field. Maybe that is what "they" are talking about... I'm off to bed and I don't want to think about it in my dreams.
Having a great time and visiting family are mutually exclusive.