While sites like Hotwire are most certainly safe, what you're looking to do, will not work.
On Hotwire.com, to book a car, after putting in your pickup and return city and dates, they ask "What type of card you would like to use for deposit." It also states:
"The rental agency will require a credit card or debit card as a deposit when you pick up the car. The card must be in the name of the primary driver, and must include sufficient available credit to secure your rental."
That means she would have to show a credit card in her own name at the rental counter, or they would not release the Hotwire car rental to her.
Before you book a Hotwire car rental, there is a section entitled Know Before You Go:
It will tell you that:
When you book the car (on hotwire.com), your credit card will be charged for the full amount of the rental car that you've booked... the total will include all applicable taxes and surcharges.
At the time of pickup, the car rental company will also require the renter (primary driver) to show a credit card in their own name. Sufficient credit must be available for a deposit. The amount of deposit varies, but will be at least the full amount of the rental.
Hotwire car rental bookings are "final (no refunds, no changes, non-transferable)."
If you book the rental and your daughter goes to pick it up without a credit card in her own name, with the deposit amount available on it, NOT ONLY will they not give her the vehicle, but YOU will be charged anyway. As they clearly state above, bookings are final (no refunds, no changes, and not transferable).
I hope this answers your question, and I hope that you and your daughter can find a way to make her rental possible. Good Luck!