Jujube wrote:But....... what if W pushes through T16? This is small right? But if now B tenuki, W ataris, then takes the whole corner! It is hard to stomach. Yet if I respond at e.g. S17, then W fixes, I'm in the same position as before but my corner is smaller!
You are correct you shouldn't let white atari in the corner, as it is big for both points and eyes for the white group and yours. So respond at s17. But you aren't quite right that after w connects against the peep you are in the same position but the corner is smaller.
First let's look at that smaller corner claim. Yes it seems like white made your corner smaller in sente, but he also made it more solid, there is now no chance for white to invade at 3-3. On move 30 there is still considerable aji for white to try something in the corner with the peep at 3-3 and p18. Now with the white two space extension on the top side still somewhat weak such an invasion, even if it lives in the corner, is not to be feared yet by black as white will damage his outside group if he lives in the corner so black can then attack that. But if that outside group gets stronger then the corner aji could be used well by white. So one could think you now have something like a 10 point corner with 100% certainty versus a 15 point corner with 70%.
Now for being in the same position, the point of the peep is that it reduces white's eyeshape in sente, so later you could have some chances to kill the white group, whereas your exchange helps white make eyeshape.
In fact I wouldn't want to play the peep, but the q14 hane after white's mistake at t15. This is another way to exploit the fact white's move didn't help r14, he can now only play r13 instead of q13. Then play p12 to seal white in, and this is sente to kill the group, and then develop the centre by attacking the top group. Another, more speculative, approach would be to refrain from making the p12 outside for life exchange and immediately attack the top group and see if you can get it running and then get some stones in the centre which means the right side group can't make eyes by running into the centre, and then kill it.