You don't say how long you've had the dog or how you introduced it to you Lab. Since you already have had the dog home for a while, it's best to use the services of a reputable behaviorist; make sure you check that they actually have training and experience; a degree in behavioral psychology is also good. Since there aren't any licensing requirements for dog trainers, anyone can say they're a trainer and a behavior 'specialist' and since you want to ensure you get help you your family and the dogs, it's best to be vigilant about who you get the help from.
Doing a little research on Barkbusters, it appears that they use positive training methods, which is good...but a couple of the comments on their website would make me ask additional questions of them. They state: "Bark Busters teaches your dog to listen in the home environment. If it does not listen at home, it will not listen outside your territory." While your dog first needs to learn while in the home environment, it then needs to learn outside the environment and with distractions. My dogs comes immediately when I call him when we're home; the first time I tried it outside, he didn't even look at me...the leaves were more interesting (and I was glad he was on a leash then). So they need to work with you or show you how to do things outside the home also. They also state: "This is where he misbehaves most often so this is where training is most effective." Dogs aren't really misbehaving; they're simply acting like dogs and it's up to us, their human companions, to guide them as to what's acceptable behavior under certain circumstances and in certain environments. Overall, the sound like a fairly good company, but as this is a worldwide sort of company as they do franchises, it's more important what training and experience the particular behaviorist who works with you has.
Most dogs, especially mid-age ones such as yours are, will have a period of adjustment, which is one reason that how they're introduced can be very important. Sometimes when they're simply tussling and deciding who has seniority, if people around them get all excited, the dogs can get more wound up and get into it more than they might otherwise have. Even dogs that have been raised together for years can get into it sometimes; many times playing turns rough, or one or both dogs can get over-excited, and one or both ends up hurt. It's up to you and your husband to control the dogs' environment. That means they shouldn't be left alone together right now; the kids should never be left alone with them (young kids shouldn't be left alone with any dog, IMO); and if the kids are around when the dogs start to growl at each other (which is their warning signal, so don't try to get them to end doing that) tell the kids they need to go to another room quietly and immediately.
Don't get too hung up on the dominance or pack stuff. While dogs may be a distant ancestor of the wolf, they are much different in behavior. New studies have shown that wolves and dogs have some similarities, but also have a lot of differences. Essentially, we do need to let our dogs know what behavior is acceptable, so if that makes us their 'leader' then it does. But rewarding dogs for good behavior, and ignoring bad behaviors or removing the dog from the room every time he jumps for 20 seconds or so, for example, can do wonders when it comes to having a dog who will be a calmer, sociable companion.
A good book to read is Dogs: A New Understanding of Canine Origin, Behavior and Evolution by Raymond Coppinger and Lorna Coppinger.
Best of luck, and please keep us posted!