I've gotten better with D1-ing people out of crossups with other my other chars (Sonya, rain) and I'm trying to translate that with Kitana. I did some testing and I can most consistently do D1, into a D1 cutter on a cross up (10%). If you want to get fancy, I was able to land D1 into 21 cutter. If you get a lot of meat on it, it can do 15%, but the height has to be perfect when you catch them with the first D1 and its not really practical in a match. D1 into 212 works as well as D1 into D1Cutter, if not better
The cool thing I found was that you can do D1 on a crossup into 2 Ex Lift. I was never able to link the regular lift. I hope this helps to anyone looking to punish cross ups with more effectiveness. Depending on the height in which you catch their jump in on D1, you can link 21 into Ex lift too.
You can link anti air D1 into B33 lift if you're a damn jedi.
To sum up, When you're in the process of being crossed up and theres nothing you can do except block or poke, I would D1 into 212 meterless, or D1 into 21 Ex Lift if you want to use a bar.
Full Disclosure: I tested this in training with the computer set to jump. Unfortunately I don't have someone I can test this with for actual crossups, though I'd be happy to on PSN if you're interested.
Edit: I've seen lots of responses in regards to how to stop them from crossing you up BEFORE it happens, but I'm talking about what to do when they actually cross you up. I agree that D1 can be sketchy. For some reason I've had better success D1'ing people out of crossups with Sonya/Rain.