It is set up the way it is because the Salute is meant to benefit primarily the servicemember--that's why it's called a salute, and is different from the (mostly) permanent discounts on tickets offered to all military/DOD personnel.
If her mother drives down to activate them, the rules are that she (the spouse) use one ticket herself (or the servicemember, although that isn't covered by your scenario). While I suppose she could essentially lie about who will be using the ticket, it is abusing the program and such abuses will eventually contribute to the program being discontinued. Those of us who use the Salute discounts to spend time with our servicemembers between deployments and 60+ hour/week work schedules get pretty upset at people who are not entitled to the discounts abusing them--the rules are clear, and no matter how many ways you phrase this question, the answer is the same: No, she may not do this.
With a DOD ID card, your friend is still eligible to purchase tickets at a discount from Shades of Green or any military base's ITT office, and she may do this for anyone else in her travel party as well.
