We will be scheduled to fly into Istanbul at 12:35 pm with a 1 hour 50 minute layover leaving at 2:25 pm on Turkish Airlines for both legs of the trip. Is the layover enough time for this connection? I've heard both good and bad about the airport and it's need to expand.
Assuming you made these bookings as one single booking,yes,it is enough time-or THY would not have accepted the booking as they are responsible for ensuring you make the connection.When you check in make sure you check your luggage through to your final destination so you don't need to collect and recheck it.
As the flight comes into land at Istanbul tell one of the cabin crew you have a shortish connection with another THY flight and ask if they can help you exit quickly(they are usually good about this).Once landed you will simply go from one arrival gate to the next departure gate,a short movement with no luggage hassles nd no need for a visa :)