No, nobody becomes a citizen automatically. You can include your kids on your application if they are residing in Canada and under age 18. They may be asked to attend an interview but they do not have to pass the test and if they are under 14, they do not have to swear the oath. If you pass the test and attend the oath ceremony and become a citizen, your kids will too. If you fail the test and do not end up getting citizenship, they wont either.
Your wife will have to fulfill the 3/4 years requirement and will have to apply for citizenship for herself.
