Remember, obedience school is more so you can learn how to train your dog, not so they can learn to be good. A dog is only as good as their owner, so as long as you're strict with them and treat them well, they usually turn out ok.
Make sure you expose the puppy to children and other animals (easy, cuz you already have a dog!) early on, that way it's a normal thing for them.
What kind of dog is it?? How old are they? You can start obedience training right from about 4 weeks old - just simple things like sit, stay, lay down. Try to start the training away from your other dog, that way they don't get distracted. Dogs can only recognize 2 syllable words consistently, so make sure your dogs name isn't long, and teach one word commands.