My mum's wedding ring

What happens if an unscrupulous jeweller doesn't melt down your actual rings, but someone else's? Is it the actual gold that's important, or the theory?

I would trust a professional jeweller to do what you asked him to do so I don't think that 'What if' is very likely

My husband has his mother's ring which he wears on his right hand.

OP I don't think there is any right or wrong here - whatever you want to do is right for you

( I am presuming here that your husband is deceased)

My wedding ring was my Grandmother's, I never knew her as she died when my mother was a teenager. I was named after her. It's a plain 22c d shaped yellow gold and I plan to leave it to DD who also has her name as a middle name. My engagement ring was my husbands grandmothers, a 0.5c solitaire diamond which dates back to the early part of the last century. That will be left to my eldest son. We joke that DH got off lightly as he didn't have to buy any rings. He didn't have a wedding ring as he had a signet ring worn on his right little finger. He did buy me an eternity ring when we'd been married 10 years so I will leave that to the youngest son.
I do feel it is rather wasteful to be buried with them and I've heard too many stories of rings being stolen immediately before the coffin is closed.

My mum was cremated that's why I've got her ring