I relate greatly to this, specifically the point that regular texts get written in stone forever. This means you can never speak freely, you must always constrain communication.
The beauty of speech is that it is ephemeral. It's okay to say stuff, ok to be a bit stupid, ok to be honest, ok to be vulnerable even. Your desire to have ephemeral messages in Signal is very wise, and only shows that you want to communicate more deeply with your family.
Of course the encryption is a bonus. I doubt your family see the value in that side though.
As a sidenote, the ephemeral communication idea, "forgetfulness by design leads to courage in sharing weird ideas, freedom to make errors", I believe is the cure for todays toxic "doubling-down" internet culture. No body remembers how to be wrong, and communities (cough reddit cough) stagnate.
I've stopped texting my friends words actually, I send them voice messages instead. It's amazing! But sorry for ranting. Hopefully I've given you some ideas of how to explain Signal to your family :)