The PA28 is not cleared for spins with anyone in the back seat; there are CofG issues that can make the spin unrecoverable. So it would not be a good idea to teach spin recognition with anyone occupying the rear (some models, and some options within a specific model, for example those with a ventilation blower in the tail, aren't cleared for spins at all).
And since a badly handled stall can turn into a spin (although admittedly, based on my PA28 experience, in which I have a couple of hundred hours, making it spin takes some effort), it would not be a good idea to practise stalls with the back seat occupied.
The issue of someone in the backseat upchucking-even an experienced pilot-is not to be neglected when doing steep turns, etc. ad nauseam. When I did my PA28 checkout many years ago (on a -181, I ended up owning a late-model PA28-140E), I did the full-up thing only near the end of the checkout doing circuits and bumps, with one friend and one air cadet in the back seat, both of whom exited somewhat green in colour due to the hot weather and turbulence, and (at the time) low-hour PPL ham-fisting it around the circuit. I've also been the ballast in the back seat for a ham-fisted pilot checking out on a Sierra (which he eventually-and non-fatally-crashed), during circuits and even though I can do modest aerobatics without getting sick, it was NOT a pleasant experience.
That said, the PA28 is not mysterious to fly; don't know which model you're planning to check out on, but you've already got low-wing experience (in a Traumahawk no less!), so I really think the instructor is wisest on this as there's little to be gained from observation. Moreover, if your friend wants to be checked out as well, it's not going to happen in the back seat for her, but in the left one. We're not talking a procedure-intensive aircraft here like a transport-category aircraft where just observing procedures from the jumpseat would be beneficial. The procedures in the PA28 will be largely similar to the Traumahawk. The only real "experience" she'll gain back there is being an extra set of eyes checking out for traffic.
That said my last check-out was when I bought my current Sundowner; but insurance only asked for a summary checkout, and the CFI that delivered the plane to me checked out my flying buddy and myself as we did a multi-stage trip to fly him home. We didn't do stalls or things like that; I had done them and full spins anyway at the pre-buy test flight, with an instructor.
Mike