If you're dad is that sensitive to noise, you're probably going to end up practicing with headphones on when he's around no matter what.

You can play it as quietly as you want; it's just that the tone doesn't get "enjoyable" until it's turned up a bit (and then improves with volume). That said, a small tube amp hits that threshold at much lower volume than a large one does. I think for daytime jamming, a Classic 30 can be totally reasonable and still have enough sauce to practice with a band, play small gigs (or be miced for lager ones).