The Insanity workouts are, if I understand correctly, designed to be done at a certain frequency. Doing them more often (and certainly if you do them twice a day) might not allow enough time for recovery.
That is absolutely correct! The Insanity workout program has been put together in a specific manner to push your body HARD while allowing enough recovery time to actually make progress. It was put together by experts, so trust them.
I've done Insanity a few times, and in my experience, if you have enough energy to do it twice in one day, then you didn't work hard enough in the first workout! And nutrition is going to be the cornerstone of your success; you can't out-train a bad diet. My advice is to nail down what nutrition plan is going to work for you that you can stick with, and DO WORK when you push play on that DVD so you know you gave it your all.