She has already told you that she doesn't want to take your recommendation. So tell your daughter that she can buy her own computer. Give her a figure for how much you'll give her to make the purchase, and leave the choice up to her. Make it something where she can reasonably do it, like $500. If she spends under budget, give her the full amount anyways.
Lots of people have to figure out how to buy computers for themselves. There is no reason that she can't figure it out. And the experience of doing so certainly can't hurt.
Cheers,
Ben