We were at the In-Laws this weekend, and they have a Lab/Wire-Hair mix that's 2 weeks older than Appa (about 6 months old) that is quite hyper. Whenever she would jump up on my wife or I Appa would have her body slammed and pinned to the ground in a matter of seconds. I can't say I don't appreciate it, but I also don't want this to carry over into other protection/possessive behaviors.

Any suggestions on how to nip this in the bud?

My sibe does this but a little gentler than Appa probably. I personally allow it because he is correcting the other dogs undesirable behavior. But I am always prepared to step in if he goes overboard. In the past when it has gone overboard I'd issue a vocal correction and refocus his attention on me. And if the verbal correction doesn't get results I would stomp of my foot near him which has always done the trick for mine. But mine has learned what I do and don't allow so he issues his own corrections to other dogs with moderate force and I am ok with it.

I'm ok with the dog correcting, but can he make the distinction of "dog jumping up = bad, kids jumping up = ok"?

He can learn the distinction just fine as long as you are consistent with training.

Excellent. Then we'll have to make sure he learns. I'll admit when I first saw it I thought "this could be handy if a dog gets loose while my wife is jogging." Not that he gets to jog with her yet, but when he's old enough.

They are really smart so he should learn pretty fast. My boy is fantastic at protection for me and my chihuahuas when we are approached by aggressive dogs that are loose. He is normally super friendly but he just instinctively knows when to kick it into protective gear and he will not back down in the face of a threat. Yet he also instinctively knows how to be gentle with children and it's amazing how incredibly gentle and tolerant he is with infants and toddlers yet he pours on the roughness with older kids. That's something I've never had to teach or worry about.