I believe you are supposed to introduce them in a neutral area (ie: not your house) that way the current dog won’t be so worried about another dog in its territory, once they have been introduced it shouldn’t be a problem to then take it home. Might be easiest to pick up the new dog and take it to a park near your home with your other dog, let them play then take them both home.
Other rules are supposed to be based around how pack animals work, so ensure the lowest ranking dog gets attention and food last. If you don’t do this the higher ranking dog will feel it needs to put the other dog in its place, which will cause tension.
Also bear in mind the top dog, sits in the comfiest/best position, and on the highest point so if you let the puppy on the sofa whilst the other is on the floor, the puppy will get a bollocking at somepoint, same as if the puppy tries to nick the seat under the table when you are eating.
As for the bond with your current dog, as long as you keep the pecking order as:
You -> Your Wife -> Your Kids -> Everything else on the Planet -> The dog -> The puppy
it should be fine.