I really want to get a second ear piercing but my Mum won't let me. How do I convince her? Please help me

The most you can do is just let your mother know that you want the ear piercing and just state your argument as to why you think you should have one. Respectfully listen to her reason why she does not want you to have one, and just politely discuss it from there. Ultimately, if you are under age, then you have to respect your mother's decision and just wait until you are old enough to get it yourself, if you still even want one when you are older.

I had the same problem! Except my mum doesn't have any problem with the actual piercing itself, just my age. I'm 13 and she said wait till I'm 14/15 and she doesn't care. The thing is at this age when we go out we represent our parents - a bit like why our school care about how they are presented when the school goes on trips. If our parents don't like it, why would they let us outside to represent them like that?
You can't really convince them. Just keep asking but if you annoy her shut up... Or she might never let you because it just shows that you're impatient and immature.
Good luck anyway xx