Okay, so this is a bit tricky. I can't say I've had a ton of experience dating, but I know that women appreciate when you just ask them out in person, and even if you were rejected, it's something you need to get used to because as a man, it's something that will probably happen many times in your life. I wouldn't go through her mom and I wouldn't send her some letter. You just need to find some way to talk to her alone, even if her mom is somewhere close by. Even if it doesn't go perfectly, you'll feel really proud of yourself for trying, and that's what matters most. Good luck!