Tell her she can friend you or follow you on all of them. That's how my daughter got hers. All she has is an instagram, if she posts something I don't like, it comes down. Oh, and I'm going to change her privacy settings right now too. This should be a fun conversation. Oh and good luck.
To convince your mother to join any of those sites, you should give her the benefits and assure her that you will not be exposed to explicit content. Once your mother is sure that you will be safe, she will gladly allow you to create any of those accounts.
maybe she's afraid for u to get a Facebook with all those stalkers and such. but u really should get an instagram and tumblr! if love to write and talk, it'd be great to share ur thoughts on a blog. instagram is fun to see pics and stuff like that! if she's not convinced enough, she should at least have u get an instagram. hope this helped!