Iowa has a "modified comparative negligence rule", which basically says that the negligence of more than one person can contribute to the accident, and if the plaintiff (you) is at least 50% at fault, the other party or your insurance doesn't have to pay damages (unless otherwise agreed in the insurance contract). That said, under the modified comparative negligence rule, if you were 20% responsible for an accident, you could still collect, but you could only collect for 80% of the damages. If the insurance adjuster is asking about who came to the stop sign first, s/he is most likely investigating whether any of the fault can be attributed to your conduct, thereby reducing their liability.
As for how they can determine that without any witnesses, it's quite possible that they can't, but they won't know unless they investigate.
As for asking you to take the photos, that is (in my experience) quite odd. To be frank, I might recommend asking to speak with your claims adjuster's supervisor to make sure that your claims adjuster is doing his/her job. Still, if your insurance contract is like most others, you have a duty to reasonably cooperate with their investigation, so if the insurance company wants you to take photos, it's probably a good idea to just do it. Honestly, it's to your advantage to take the photos yourself because you can make sure that the angles, lighting, etc. are most favorable to your case.
I hope that your daughter recovers quickly. Let me know if further clarification is needed, and please feel free to leave a rating once you are finished. Thanks.