It seems to me like the meeting/greeting stage is progressing pretty normally.

Just make sure that both dogs have plenty of room to get away from each other when they want their space. To have one or the other confined or restrained may cause even more defensive behavior (just like having them cornered would). I don't usually interfere until they start snapping (unless we're visiting at someone elses house); one dog will learn to respect the other one's growl (it's just like your verbal correction, but in dog language). I'm lucky enough that both of my girls have 'handles' (tails )that can be safely used to separate them when it gets ugly, so that I don't get bitten.

They will learn to like one another, but there is definitely a process of establishing the pecking order between them, which they have to do themselves. Since one of yours will be so much bigger than the other, you may want to intervene sooner than I do so that Bailey doesn't get hurt, but let them get themselves sorted out. Just make sure they both know you're the boss and can enforce that position by all the techniques that are commonly discussed on this board.

Oh, and post a picture of the new pup if you get a chance