I mean, they can slip a little if I don't lace them snugly. By snugly, I don't mean painful or cutting off circulation, but just tight enough.

It makes sense that your dad's shoes trip you up. Assuming you are a 9.5 in heel-toe and arch, and a normal width, then your dad's shoes are 2.5 sizes too big for you in every dimension. You probably couldn't tighten them enough to keep them on! But I'm only 1.5 sizes off between my toes and arch. If I'm 9.5 heel-toe, then I can wear a 10.5 or 11 properly thanks to my arch.

The real problem is that they don't make shoes in unmatched dimensions. I either have to have a little extra toe room, or have my toes get squashed in because of my arch. The latter hurts and will deform your feet after a long time, so I'm done with that.