I think if she's underage she can.
Are you underage Mish?
Actually a joint bank account gives both the parent and user access to take out and deposit money. It sounds like the mother is the primary account holder though.
One option is to open up a new account without a parent. Some have a small requirement of depositing twenty-five dollars by a certain time to open the account. The only problems I could see with trying to do that is not reading the fine print when you open one up. Some accounts require for there to have a minimum of one hundred dollars in the account at all times and the other option has no set amount but will kill you in overcharge fees if you happen to write a bad check.
Another downfall is that certain banks will not let you deposit more than one thousand dollars at a time until a certain period passes (6 months). So in the instance you had to deposit more than that, it would probably be a good idea to talk with the financial institution first.
Some other questions to think about:
-Use a local bank or nation/global wide bank?
-Do they have a good reputation in customer service?
-Is the person that helping you open the account giving you time to read the fine print and knowledgeable about the questions you ask them?
-Is the institution an FDIC member? Federal deposit insurance protects the first $100000 of deposits that are payable in the United States (FDIC.gov).