I have mailed my neighbors my native fruit, but they still won't give me..

You can never be certain what your neighbors will send you. If I'm eyeing something in thier house that I want (bed, chair etc) I'll send them another in a different style hoping they will give it up. Sometimes, sometimes not.
Fruit, I have found is really random. I actually had all of the foreign fruit before my peeps started sending it to me. Your "mom" in the game sometimes mails foreign fruit as well. I would suggest going to the forum and getting a friend code so that you can trade fruit. My friend and I spent a long time one day just trading all of our fruit for big bucks!