You're talking a few different scenarios all at once, so let's try a little divide and conquer.
If you've gotten into a turn a little hot and don't think you can make the apex without scrubbing some speed, dragging a
little bit of rear brake (
only) can help tighten the line up without washing out the front. If you're truly too hot and can't turn more, using the front brake will be a disaster. The front tire will already be near its traction limit and asking it to do some braking in addition to cornering will overload it and you'll low-side. Prior to the apex, you'll just be using maintenance throttle (maybe a hair more), so reducing throttle input will not accomplish much, and if it does it may transfer too much weight forward (low-side again) and in any case it is likely to be abrupt and unsettling. You can be smoother and more precise with the rear brake than with the throttle.
Learn this technique when you're not at the limit first!
If you're already down near the apex and realize the turn is tightening up on you (decreasing radius), you still have plenty of lane left to work with on the outside. Stand the bike up momentarily, brake as you approach the outside (i.e., center line in a right hander), then turn in again. Essentially you make the curve into a double apex line.
Obstructions in the road are a whole different game, and what you do depends upon what's in the road and what it's doing. In most cases you'll need to get speed down quickly. If you're on a good line and looking as far around the curve as possible, you'll probably have some lane space available to let you stand the bike up and brake. Once you have some speed knocked off, you have more options in maneuvering the bike. Fixed objects, like a rock or log in the road, can then be ridden around. If it's a large animal,
STOP if at all possible. Frightened critters are unpredictable, and if you try to go around they're quite likely to dodge into you.
Encountering a deer in the road, mid-corner, is one of my worst nightmares. I was in a curve near Elijay, GA, some years ago, and came upon a couple of does in the road. I was able to get the bike stopped, thank God, but it was a while before my heart rate got back to normal. Animals can leap in front of you without warning and sometimes there's not much you can do.
If you're at Deals Gap and encounter a large truck occupying both lanes in a curve, likely nothing you can do will work. Just try to get in a quick prayer before you die.
Overall, the best advice I can offer is to get this book:
http://www.amazon.com/Sport-Riding-Techniques-Develop-Confidence/dp/1893618072
and read it cover to cover. Then read it again. Then go practice. Then read it again. Then go practice. Then read it again. Then go.....
I've been reading and re-reading and re-re-reading that book for years. Even when I know what it says, I still read it again just to keep everything in the front of my mind.