I remember you making a comment about it being awkward and weird that I asked my mom for a packer! It's not weird and awkward when you have a good, close relationship to a parent. I figure, they have seen us naked since we were kids and they know us better than anyone else.
Just be honest with her. I'm sure she knows about your transition. I'm not sure, I can't remember. So yeah, tell her why it's important for you to get it. Tell her how you feel without it. If she understands what you're going through with the transition, then hopefully she will understand why you need this.
All I did was tell my mom I wanted a packer and she was way more cool with it than I thought. Parents have a way of surprising us. So maybe you should just go ahead and tell your mom. What's the worst that could happen? She says no. So you find a way to save up money, and buy a pre-paid Visa and get it yourself.
*Edit*
I see you say you have the money to pay for it. So if you want to just avoid this whole thing try and see if you can get a pre-paid Visa and make a paypal account. Best of luck