I put my insulin in my hand luggage where it has always been fine (I have flown over 100 times with insulin).
I never carry a separate bag for medical supplies. This is as much about finding it easier to get around with one bag than two and not taking that much stuff (even when I travel with hand luggage only).
I have read that some airlines allow extra hand luggage as you say but it may be worth checking with your airline as they probably differ.
I never put any of my diabetes kit in the hold. Insulin could get too cold and stop working. But the main reason for me is that my luggage has gone awol a few times and I would hate to be without my supplies for an unknown time.
One thing to consider with Frio pouches: I never "charge" mine until I reach my destination. The reason for this is I have heard some security are nervous about the gel in the pouches when water is added to the crystals.
Provided you keep your insulin out of direct heat, it is not damaged for 24 hours at room temperature.
Finally, I recommend taking a letter from your doctor. In nearly 15 years of travel with diabetes, I have only had to show mine once. However, that doesn't mean it will be requested again and I wouldn't want to lose my insulin or not be able to fly.
