Of course he wants to come inside - that is where you are!
Dogs need the company of their family - especially if he is your only dog keeping him alone outside is quite cruel. Dogs are pack animals after all.
1) If you really cannot keep him inside the home because of the allergy, and only want one dog, just find him a new home. It is fine, really! For both you and the dog that is the best in the long run.
2) You have a puppy - do pamper him a bit! Dogs are fully grown up when they are about 2-3 years old. Right now he has to learn everything - who you are, where he lives how to communicate with dogs, with you, with cats, postmen, etc. He won't learn that in a way that satisfies you if you do not guide him. And guiding a puppy is more or less a full time job for the first 6 months. You wont be able to teach him everything he needs to learn unless you move outside for most of the day, to spend time with him.
3) This seems to be your first dog, I would recommend reading up an a dogs body language. This is his main way to communicate with you, and you need to be able to understand what he is saying in order to train him.
4) Your dog will at most have the intellect of a two year old. Keep that in mind when communicating. I find training with the clicker method the easiest to make myself understood, and especially young dogs love it.
5) Concerning hygiene - dogs do clean themselves, and a healthy dog is no health risk whatsoever. Getting a dog houseclean is some work, and there will be accidents in the house, but unless you plan on licking the pee and not washing your hands after cleaning up, there is no health risk.
6) Concerning the allergies: I am allergic to animals myself, also my dogs, so I know this can be annoying when handling them. We got a breed that looses little fur, so this is not so much of an issue. However, only your wife really knows how bad her allergy gets. If she gets asthmatic around the dogs, I would recommend re-homing the little guy. If it is only slight itching of the skin, she has to decide if she wants to put up with that. Since the allergens are in the saliva of the dog, it is rather easy to handle. After interacting with the dog, just wipe down the parts you got in contact with, with clear water. But again - I think she needs to be ok with this. I know how annoying having a pet with an allergy against it can be. And 10 to 15 years is a long time to live with an animal you are allergic too, and wont work if she is not on board with it.
Hope this helps. Let me now if you have questions.