So you just want to convert it to usd and make it as a proof?
You dont need to do it.
Show your mom videos about bitcoin from well known news media channels.
It would make her thinks that bitcoin is a legit thing.
And then let her know about bitcoin.
Final step, show her bitcoin success story video.

But if you still want to convert it,
Just search on facebook, a bitcoin local enthusiast group.
Please be selective on finding it.