My mom says that I'm not allowed to be braless under clothing, even if I'm in pajamas ready for bed, because my dad lives in the house. Is she being paranoid?

Unless your top is not transparent I don't think it should be a problem. And I think if that's the case then I don't think it doesn't matter if that's your dad or your mom, you wouldn't like any one of them see what's under your top or pants, right! You see for yourself, if you feeling awkward wearing what you are in front of anyone, then I am sure you yourself won't. Having said all this, ask your mother in detail, what is going on in her mind. She too must be having some valid point, after all, she is been through the age you are in.

I think it depends on individual family upbringing. But if you ask me, I personally feel that anything within the house with just parents and siblings should be fine. As long as not totally naked. Not wearing bra at home is perfectly normal. You ask your mum does she wear a bra at home. If she don’t wear, means you also don’t wear. I don’t think it bothers your dad unless he himself is the pervert kind of guy. Usually fathers and brothers at home don’t really bother about whether the ladies in their house are wearing a bra.

I think she is. It is your dad, after all. Unless she doesn't trust her own husband. If it makes your mom so uncomfortable, when you are not in your room, maybe throw over a cardigan or hoodie over your pajamas. That's what I do if I am at home and if my parents or in-laws (or pretty much any other guests) come to stay.