The only trouble....many toy breeds are bred for companionship. I'm thinking of my Chihuahuas, for example. And they would be crushed little souls if left alone all day every day. So would any breed, but most toys are very dependent. And they have to be inside and highly supervised when outside, as there are birds of prey to watch out for and other animals. So, they too, take a lot of attention.
Bigger dogs do need exercise and lots of it and obedience training. And like everyone said Katie, they need to be with their families. Labs were bred to work along side man, to do everything with their person and are quite dependent on family. They're known as a "family" dog. I had a Lab and if I had left her outside and not spent very much time with her, she would have become bored, destructive and unmannerly. She would have been miserable if not allowed to be inside, lounging near me or in front of the fireplace. The dogs I have now; two Chihuahuas and a Doberman....same thing. My Doberman was bred to protect his person or family and he HAS to be near me most of the time. He's a lovely dog and happy. If he were left on his own outside without human contact, he too would not be the same dog who he is.
Most all of the behavior problems you speak of are due to the relationship your dog has with you and your family. The skills to not jump and other things can be taught quite easily. But not if the dog is outside all the time. He can't get the hang of what it's like to live in a human's house or with humans....learn our ways of being "civilized" if he's not allowed to practice or experience that on an ongoing basis. Dogs are animals, not humans. They don't automatically behave mannerly to our ways. They do what dogs do. And until the dog is allowed to partake in a family life, he will remain very much in a state of doing what dogs do and that is all the stuff we don't like; jumping, peeing inside, marking, taking things, chewing up things, destroying stuff, pawing at you, biting.... etc...
If your folks don't want the dog to be with the family when you all are at home, then I would have to agree that a new home and new family would be the kindest, most unselfish thing you could do. Perhaps cats are a better pet for you, as they are quite a bit more independent, needing to socialize with people, but not quite so intensely or closely. Dogs were pack animals and as such must be with their human "pack."