Sorry to hear that Max. FWIW, I doubt whether the bike could be the fundamental problem - at best a perfect setup might alleviate her problem, and make it less likely to recur after she recovers. But it might just be that even though you guys are such youngsters, going out on a cold January day isn't the best way to recuperate? Injured joints and ligaments don't like the cold, however young you are.
In terms of an ideal setup, I would say she looks comfortable on the bike and the size 16 Hahanna is really quite a small frame, c525mm top tube c-c I guess (that's a half inch shorter than a size 16 Explosif or Cinder Cone). Anyway, even if the top tube was too long, I don't see why a longer top tube could aggravate a knee problem - if anything it could even help.
It might help if you could show us a picture of the bike, but without seeing it I would suggest that you look at the cranks, the saddle position and the weight of the bike. As has been said, for Heidi's height a 170mm crank is the maximum, 175s are designed for six foot tall men. Combined with that I would look at where her knee is in relation to the pedal with the cranks horizontal. The centre of her knee should be above the spindle or even slightly forward of it. This may require a straight post rather than layback, and the saddle a bit forward on the rails.
I think the theory behind that is that the 'race' position is the most powerful, with the best angle for the muscles to work and enables you to put your weight into the stroke, taking the strain off your knee. Although females often feel more comfortable and relaxed in the further back position, it is fundamentally weaker and puts all the strain on the muscles and joints, especially on climbs where the weight is even further back because of the incline. Bar ends could also be beneficial for this of course.
And then finally the Hahanna may be pretty but it is quite a heavyweight. If you could find her a size 16 Kula or Pahoehoe frame, it would be about 2.5lbs lighter, have better power transfer and cost you £75 maximum, maybe less. She's worth it! Come the warmer weather when the knee is well recovered, she could maybe have a go on my KHS TiLite if she'd like to see whether a light bike would help.
Apologies if you know all this already, but hopefully some food for thought in it somewhere.