Dogs don't experience jealousy. You are humanizing an animal, and that is often when animals misbehave and get confused about their role in the pack (i.e. in your household/family). When dogs get confused like that, this is when they dominate and destroy things, because they start believing (b/c of your projection of emotion and energy) that you are actually following them, so they become your pack leader, they run the show, everything around them is owned by them, it is their domain, and they can destroy it as they please.
I suspect your dog is acting this way because he has too much pent up energy, typical of breeds like Boxers and Jack Russel Terriers, and he has not properly been given proper rules, boundaries and limitations. High-energy dogs like this require a minimum of 20-30 minutes of disciplined walking per day. Walking and letting the dog lead you, pulling you around is not an example, I'm saying, you need to be correcting the dog's tugs and asserting yourself as the leader of the walk, from the moment that you walk out the door before him on the way out of the house, to your walking in the door before him on the way in the house. If you ever let him lead or pull without correction (a slight tug or touch of the foot), you are allowing him to test his boundaries, and establish that he is supposed to be controlling that activity. Dogs establish boundaries like this in nature. It is very different from humans.
Also, back yard is NOT a walk, neither is playing fetch, the walk is an exercise of both control (you controlling the dog), physical relief (energy exhaustion), discipline (tasks during the walk) and adventure (mental exhaustion). Regardless of how big your yard is, you must understand that your dog sees the backyard as an extension of the house, your shared house. You can accomplish wearing him out (energy exhaustion) by playing ball with him in the backyard, but you are not giving him any disciplined challenge (games are not discipline IMHO), and you're definitely not providing an adventure to exhaust his brain.
Ultimately, with no real leader, a dog will pretty much do anything they damned well please. Everyone in the dog's life MUST be seen as a pack leader by your dog, or your dog will quickly get this idea they're the leader - dogs live "in the moment", they don't remember what happened yesterday, this idea of being pack leader can transition in less than 15-20 minutes of being with a submissive person who is not taking a leadership role.
Someone mentioned Cesar Millan above. He would probably tell you something like, "This is not dog obedience, this is simple dog psychology." I like his mantra, "Exercise, Discipline, Affection, always in that order" Without at least 15-20 minutes of all three of these per day, your more hyper breeds will instantly go from calm, submissive state to more of an anxious, fearful or aggressive state.
Dogs are not human beings, and do not have human emotions in the way they're being depicted by many human owners. It is very important you do not think of your dog as a human or treat your dog as a kid. Especially with high-energy dogs, it will lead them to a persistent state of anxiety, fear and ultimately end up aggressive, which is not conducive to an environment with a baby.
FWIW, I have dogs, rescues that had serious problems which were promptly fixed using a lot of methods that Ceser explains, and we're about to bring a kid into the household as well, with a dog that was child-aggressive in the past (due to fear of them). Mr. Millan is a good guy to watch. Buying a couple DVDs of his show should be a mandatory pre-requisite to dog ownership. The guy knows his stuff, and humans really don't understand the psychology and needs of a dog, but prefer to treat them as a human family member, which is unhealthy for the dog and the family.
Human projection doesn't stop with love. People who think "time out", yelling, spanking or verbally scolding, ignoring or getting angry at dogs is some form of discipline for dogs couldn't be more wrong. These are all "human" ideas which should be applied to humans. Dogs learn they are doing something wrong by correcting them in the act, and repeating this correction many times in a short period. You do this by challenging them to perform the task, and correcting when they try. These types of exercises to form limitations, rules, boundaries are all very healthy for a dog.
Even the smallest task is helpful in establishing dominance. Like forcing your dog to sit at the door while you walk out of the house until you tell them they can come outside, and vice-versa on the way in. You should always control activities. Dogs actually LIKE someone controlling them, and will love you for doing it properly.