As beneficial as adding in some weight training to her program would be, I'd stave off on it until she can increase her flexibility enough to get a better ROM on the lifts. Without having the ability to achieve full ROM, she runs a much higher risk of injuring herself.
From the sounds of it, she's one of the more extreme cases of having an overly tight posterior chain. Most people do, just not quite that extreme.
If the treadmill sessions are working for her now, have her continue those, and at the end of every session do a full series of static stretches. She can even stop in the middle of her session and run through some stretches then do another set of stretches at the end of her tready session.
Give a look at the stretching and flexibility thread on here:
Mainly the section about achieving the splits. Those stretches are geared toward the lower body with some emphasis on the posterior chain and low back.
If she sticks with going through this process 3-4 times a week, she should be able to get at least to a parallel squat within a couple weeks' time. Once she's reached that point, she should be better able to handle a lifting program. And she'll be able to work all the way into an A2G squat once she's better conditioned to the movement and her posterior chain loosens up.
Now when she starts going through these stretches, she WILL get sore. Sounds odd, I know. But it happens. Just be prepared for her to tell you all about the hurt
Rippetoe's program is a great one for beginners. So once she's comfortable with the lifts (and you too, being that you'll be guiding her) working her into that program should prove to be fairly beneficial for her. Start her off with lighter weights, though. As in, if you're doing a 3x5 setup with that routine, have her work with weights that she could most likely rep out 8-9 with. Have her stop at the 5 rep mark, just go easy on her exertion levels for the first couple of weeks.
Not sure how you're setting up your own frequency with that program, but for her I'd say during those starting periods (2-3 weeks) only have her do a 2 day a week cycle (some people do an A, B, A one week with B, A, B the next). Workout A and workout B once a week each. And not back to back days.
As she progresses, and once she gets to working with weights that more closely fall in the 5 rep mark, then you could try working her into a 3 day a week lifting program. But if the two days a week are working well for her, don't fix what ain't broke. ;) Let her ride that newbie effect as long as she can.
Also, once she's moved into the lifting program, have her back off a little on the cardio. 2 days lifting and 2 days of cardio should suffice.