It sounds like this is a regular exit for you that you take often.
What is going to help you is experience. In order to be able to recognize when the bike can handle more brake or not, you are going to have to be able to remember how the bike feels in different scenarios. I would try different drills on a familiar "clover leaf" turn. You must remember road conditions change with temperature, oil, water, etc.
Make sure traffic is light or nonexistent. You want the road conditions to be clear and clean. You are starting the drills at a slower speed and finishing the drills with a normal speed.
Enter the turn with the throttle closed and then twist the throttle open a little after you initiate/enter the turn. Then try again
This time increase your speed a little bit so your throttle needs to be opened a little when you are further into the turn, then try again.
Once you get the hang of having the throttle closed and not using any brake a few times, using the rear brake only, try dragging your rear brake ever so slightly for just a little while, before and into the turn, turn the throttle back on nice and easy while releasing the rear brake. Use the speed you had in the first drill then increase your speed a little when you feel comfortable.
Ideally you should be using the front brake, but this is a drill without traffic around. You are trying to understand the feeling. So at first you are practicing throttle control with no brakes, then just the rear brake. Next you can do the front brake.
Enter the turn with a normal amount of speed. Use the front brake like you normally would to initiate / enter the turn. When adjusting your speed for the turn, make sure you are nice and straight/upright. Ease off the brake but not all the way, carrying a little speed as you begin to lean. The idea here is to have the bike leaned over while still having a little bit of pressure on the front brake. When you are trying to get the “right” speed for the drill, do not reapply the brake. You should be doing all your slowing down before the turn like normal. You are going to just hold the brake a little longer and a little lighter, correcting yourself with the throttle. Remember, you can do this drill because you already know how to “catch” yourself with the throttle from the first drill.
After practicing these drills in order and over a few days, you should then be able to try applying the front brake mid turn. The thing you should be remembering is your sense of speed when you were practicing the other drills. What is going to feel different is the fact that your bike will want to stand up as the braking becomes stronger. You also have to remember to allow the bike to stand up by not forcing it, not pushing or pulling on the bar. Fighting the bike’s natural tendency to stand up will diminish the amount of available traction in the front tire. As the bike slows, you need to gradually apply more brake. Increasing the brake pressure, relative to the bike slowing down, is going to offer you the “stable” feeling. If you are not feeling the bike gradually standing up, you are not applying enough brake. The other option is to “catch” yourself by turning the throttle back on. If you are done slowing down or you no longer need to stop mid turn, you need to make the bike stable again with the throttle.
The last step would be to use the rear brake. The rear brake should be initiated before the front and while the bike is in an upright position. The action of shutting or chopping the throttle causes the rear wheel to slow down due to compression. Judging the amount of available traction the rear tire has while leaned over can be very difficult, especially when combing the use of the rear brake with closing the throttle. This is a good reason to wait until the last possible moment to pull in the clutch before a stop. It is not impossible to use the rear brake, just important to understand and have the experience to recognize the many factors which determine the available traction.
Good luck and I hope this makes sense.
You gotta crash first before we answer questions here! Just kidding, but I agree with Squid Vicious and the other posters, you should be able to use the front brake alone or in addition to the back, even down hill and in a turn under normal street conditions. 
