New puppy's first day home!

Just supervise their interactions.  I'm thinking the older dog was delivering a message to the pup, and I don't doubt that the pup heard the message loud and clear.  Us people don't have a clue what was being said, but the dogs sure do.

I suggest you do absolutely nothing when it comes to pack position.  This is something the two of them will work out over time, and human intervention doesn't allow the fluid change of position that occurs naturally.

Thank you! This is great advice...it is nice to know that what should occur, will occur naturally for the most part. We don't want to mess anything up! We just want them to be buddies one day!  =)

We had the same kind of setup you have : a 2 year old spayed female and a new female pup.

Spip took way longer than your older one to even consider playing with the "intruder". One thing we did was to provide some alone time when pup was sleeping in her crate in the house and Spip was outside relaxing with us and we tried to keep part of the daily routine stable. At first, I did not want to be alone with both; the size difference just freaked me out because Spip could have done that pup in so quickly. It took a couple of weeks to have appropriate interaction develop and by now (three years later), they are doing more than fine together. So you are ahead in the game compared to where we were

Like Glenda said, supervise interactions and keep giving the older one "puppy free" time. .

When we introduced Kenya and Coke, we did it at a neutral location.  They basically walked around and sniffed each other, but otherwise ignored each other.  They were fine during the car ride home.  We took them for a short walk and let them sniff around the yard and they were fine.  Inside, Kenya (the first dog) wanted more personal space.  She was a little possessive of her crate, her toys, the couch, and the bed.  Luckily, she gives a LOT of really obvious visual warnings, namely curling her lip.  I suggest you never correct those behaviors (lip curls, snarls, growling) because they are warnings.  Correcting them means the dogs will stop doing them and instead just go ahead and bite.  The only time I corrected Kenya was twice she nipped Coke's ear and he yelped, so I said said "eh eh", asked her to go to her kennel, and pet Coke.  They were both a little guardy of their food.  What we did (and still do) is feed them in their own crates at the same time so they can't bother each other.  I also did a LOT of sessions where I sat between them and just hand fed them treats back and forth.  I would slowly move them closer and closer.  Now, three weeks in, I can have them lying down so that they are leaning against each other and hand feed them both.  After a few of these sessions, the food guarding stopped.  They both realized that 1) *I* control ALL food and 2) they were both going to get some so there's no point in guarding it.  For the first day, we did a lot of trading spots - having one dog crated while the other was free and then switching every half hour or so.  They've never had an incident while walking, so we took them on walks together.  For the first few days, I supervise ALL interactions.  I kept a drag leash on Kenya so if she got snippy, I could pull her over by me.  Once they went 24 hours with no incidents or "back off" warning signs, I let them be out together and wasn't as careful about following them around or keeping them by me.  For the first week or so, Kenya would still curl her lip if Coke came too close, but he understood and never got pushy with her.  Basically, he decided the pack order and chose to be the submissive one.  As Glenda says, I did not try to manipulate their pack order.  Kenya is the alpha (again, Coke basically chose to be the submissive one) so I would never do something like make Kenya roll over in front of Coke or force Kenya off the couch and let Coke on.  Basically, I let them interact as they pleased and communicate as they pleased as long as there was no biting.  Outside, they both like to play pretty rough.  When one dog is sick of playing, s/he will let the other dog know.  Again, I don't really have to step in because they understand each other's communication.  When Kenya snaps, Coke knows she's done.  When Coke growls, Kenya knows he's done.