AAHHHHHH! you're scaring me! Your 3 year old sounds like she is allergic! Gagging is a major symptom. My twins are both allergic. Peanuts could kill your daughter, you should take her to be tested immediately!
As for your son, the reason they say to wait until 3 is because 1) at that age they are better able to tell you if something doesn't feel right in their mouth ie. an allergy, and 2) because waiting till 3 gives them more time to build up antibodies so that they are not allergic.
Obviously if your son is already eating it with no problem, then it's fine. But for your daughter's sake, you should get peanuts and peanut products out of your house.
The first few times my kids tried peanut butter, one only had a small reaction (slight gagging, making weird noises with his mouth/tongue), and the other 1 had no reaction, he just spit it out and said he didn't like it; but they are both allergic! And the more exposure they get to it, only makes the reaction worse; ie. the first few times were a mild reaction, the next time could be fatal