Dogs are pack animals, and they want to maintain their place in the pack. We all know some dogs that are more dominant or submissive than others. When we got our dog, as a puppy, we took her to training (more for us than her). Ours is a large mixed breed mut. Most were pedigree. The most mild-mannered was the Rottweiler, and the most dominant was a small lap dog. Go figure. Just like us, though, they have their own personalities.
We had it all figured out until our kids came along - so did the issues. I'm alpha. My husband was next, cat, then dog. Then kids come along and challenged our dog for spots.
We had to see an animal behavioralist because of thousands of dollars in damage to woodwork caused by our dog's separation anxiety.
So, my thought is that it's partly loving, partly protective and partly to see how they can maintain their place in the pack (especially since this is a grandchild and not a child in the home permanently). I don't think they'll cause any harm - it sounds like they're well trained. But, definitely keep an eye on it. The age of the dogs, their tolerance for "loving" from a child, what breed (some are instinctively more loyal and protective than others) will all be challenged as the baby gets older and more interactive.
Our 2 year old cries about every other day when the cat has had enough and scratches her. It's not the cat's fault, and we're to the point that we've told her time and time again to leave him alone. When she pushes, he pushes back, and she'll learn one way or another.