I think that stuff like that is different for every organization, or even for every chapter. I will say that lavaliers at least are usually reserved for girlfriends/fiancées/wives, not daughters. So that might be kind of weird.
As for t-shirts, that really will depend on campus/the national org. On my campus, if you're wearing fraternity letters, they're either your significant other's or they're on a borrowed shirt from a late night "adventure." If this is the case on your campus, I probably wouldn't do it, even if it would technically be allowed. It could just get really awkward really quickly.
For what it's worth, my dad's a Phi Delta Theta and I would feel extremely weird wearing his letters/other insignia (if I would even be able to). I would feel just as strange doing that as I would wearing my mom's Chi O stuff...they're just not my letters.
If it's a normal thing on your campus and you're going to do it, I'd definitely opt for a shirt over a lavalier.
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