I'm not going to provide tampons for my daughter
Why wouldn't you buy them for her?
Because she should buy her own and I want to spend my money on something else.
Well, if she doesn't actually need them then I could understand, but you are responsible for providing for the tampons as she does need them. Don't make her pay for something you should be paying for.
She has money. She should pay for it.
Tampons are a required health item for your daughter and it is not her responsibility to pay for them. Not paying for them is an abdication of your duty as a parent. Do the right thing and cover her basic expenses.