I have used my QF points on both EK and QR and AA or BA miles on QR when traveling to Turkey over the past few years multiple times. I generally build in along enough layover to take the public transport to the souk (I am married but sometimes travel alone) for some quick shopping. Sometimes I stay overnight to avoid arriving in Istanbul completely exhausted after 16 hours in economy seats. I have never felt unsafe in either country. But I am also a well-experienced traveler and had been to over 180 countries before your daughter was even born. I know how to handle myself and I accept that some aspects of travel hold some risks.
No one can predict the future but after the worldwide outcry over what happened, I think the airports will probably implement a protocol in case something like that ever happens again that will not involve invasive personal searches. I didn't know that DNA testing had advanced enough to give such quick results, only just read this above. I did a DNA test on Ancestry.com for geneology and ethnicity and it took over 2 weeks to get the results. But hopefully airports will now keep rapid tests on hand.
I can imagine discovering the attempted murder of a newborn baby would have caused panic amongst the security guards who discovered her and their first reaction might have been "Crime committed, find the culprit". But they made very bad choices in HOW they went about trying to find the culprit. At the very least, these guards should be sacked for incompetency and all others given proper training. Properly trained guards should not panic even in extreme situations and there should be supervisors on hand to manage investigations and take responsibility for doing these bearing in mind basic human rights.
I am not an expert but I think they should have been more transparent and used observation skills to try to narrow down the culprit. Firstly use the manifests to try to narrow down the suspect list. A lot of passengers could be eliminated based on age, married/traveling with spouse, ethnicity in relation to the baby. Then send people trained in body language observations to board the planes, tell the truth about what happened and observe the reactions of the remaining suspects. The body language and facial expressions could give her away. Then offer choices to the women on how they can exclude themselves from the suspect list (they had not given birth within x hours). Let them choose between examination by a female doctor/nurse, DNA test, blood test or whatever methods worked.
Maybe people who have experience can suggest how the investigation of attempted murder of a baby can be conducted without violating human rights? I am only guessing really, I don't know.