Adding Another Dog

How long have you had Molly? If she is a relatively new addition to your family, I suggest waiting a bit longer until she is completely settled. A big change such as taking in another dog (a puppy at that) may stress her out as the routines in your household will definitely change.
 
Why do you want to adopt this puppy? Is part of the reason its "short lifespan"? Please remember that a puppy is a lot of work and requires constant supervision. With proper care (as it should be), a dog will live until, or sometimes even past, sixteen years old -- and it is unnatural for a dog to have a "short lifespan".
 
You said you are a little anxious about this decision, and I think that speaks a lot about your natural apprehension towards adopting this puppy. You mentioned that Molly tends to be too energetic/aggressive around other dogs, and your puppy will certainly be one of those "other dogs". You cannot ensure one dog's compatibility with another, and the only way you'll find out if they'll be okay is if they actually meet. Please get Molly's approval too if you push through with your decision.

Molly is 3 now, and we've had her for all but 2 months of her life. So we have a good routine set up. A huge amount of her energy/aggression has gone away since we have a yard to play with her in (it has been a very dramatic change).

We raised her from a puppy, so I'm  familiar with the effort it takes to raise another puppy. My wife and I are lucky enough to work often from home, so we aren't too worried about raising the puppy.

I'm mostly unsure how a new dog will change things. How long does it take two dogs to establish their natural pack order?  Are there any other benefits that getting another dog would have, other than just having another cute, friendly animal in the house with us?

Welcome to the forum! 
 
Wait till the pup is at least 9 weeks old.  Then have Molly meet the pup on neutral safe territory (some place neither will think is theirs and is safe from outside diseases).  See how they react on leash (not a direct approach) then based on how they do you can allow off leash interaction.  Go home and decide whether or not you, your wife and Molly really want this one []. 
 
If you do decide to take the pup be sure to socialize him/her since it sounds like Molly did not get much in the way of socialization to other animals.  Please - I am not criticizing you, I made the same error with my first dog as an adult.
 
Good luck and let us know what you decide.

Getting another puppy was the best thing i could do for my dog! I was thinking about getting one, but i didn't know how my first dog would act. I brought my mom's dog over to my house, and he acted really agressive towards her...I thought it could be because he used to live with her, and she showed dominance over him. I was very nervous...but i still wanted the pup. I lined up a home for him, in case my dog didn't like him and brought the puppy home, and it was one of the greatest things i've ever done for him. He has a constant playmate!

Getting another dog is work, but, since you've already got a routine down, it shouldn't be that bad...once you get the puppy trained. 
 
I've had two dogs my entire life and while they are a handful, they often times will keep each other company which is great when you're busy doing things and can't give them full attention.  
 
You've got a house, a large fenced yard, and your current dog is already 3, so I would say, do it....if you're getting the dog because you want the dog, not because your relative is pressuring you to take one. 
 
Just be sure to ease the puppy into your family by introducing it to your current dog, and praising your current dog for being good when its passive, not aggressive or mean to the puppy. 
 
Finally, the pecking order of alpha is going to fall to you since you're the true leader of the pack.  But after that, you'll have to see how the two are around each other.  At first the older dog will likely be the beta.  But once the puppy gets older, the roles can switch, but you won't know that for a few years.  You can try to maintain your current dog as the beta, but when you're not around, their natural tendancies will come out.
 
Best of luck...!! 

How do you know this dog has a short life span? What breed(s) is the pup?

I think the OP was saying "short life" in regards to being a farm dog.  Lots of dangers involved when you have an unsupervised dog running around on a farm.

Yep. Farm Dog = Short Life

Due to rat poison, other dogs, cars, machinery, etc. etc.

I'm very glad for all of the responses here, but I think my wife and I have determined not to get this puppy. While our hearts are very much agreeable to the idea, we're in such a good place with Molly now, and we'd hate for her to regress to her previous lifestyle of aggressive barking and constant, nervous energy. It is just too much of an unknown bringing a new dog in since Molly has finally become much more friendly and outgoing towards guests, and even strangers.

My wife just got off the phone with her sister, who was in tears when we told her we weren't taking the dog. Tough times, cute, friendly puppy, but we really have to respect our feelings of anxiety over getting the new dog.

I think getting another may be just the right thing for Molly.  If she accepts the puppy, they will wear each other out playing.  I suspect in your apartment, she did not have enough to occupy her mind..
 
I really regret that we didn't have 2 dogs for most of Holly's life.  2 dogs keep each company and out of trouble when you leave the house. It is a little harder to walk 2 dogs on 2 leashes, but I manage.
 
I would get a male for the 2nd dog .  I'm sure Molly will always be top dog!

Welcome to the forums clownsaw!
I think you did the right thing. From your first post I felt your hesitation came through pretty loud and clear... there will be opportunities to add a second dog in the future, but if it doesn't feel right now, it probably isn't.

Did you ever take your first dog, Molly, for walks or to the park?  It sounds like she needed to get outside and get some exercise and thats why she changed when you moved and got a backyard.  If you are not capable or willing to exercise your current dog other than letting her play in the backyard, you most definitely shouldnt get another puppy to deprive.

Good to hear that Molly is doing well and taking to your new house!
 
We just went thru the process of adopting a 2nd dog after having our older dog (as an only dog) for 8 years of her life.  We put alot of thought and effort into bringing a new dog into the mix.  Ponce (our older dog, 90 pound lab/greyhound mix) was secure and happy in her routine and in our life.  We didn't want to ruin that.
 
If you want to follow our successful plan of attack, here's what we did:
 
We started by observing Ponce around other dogs.  What types of dogs did she like?  What types did she NOT like?  We learned rather quickly what traits Ponce looks for in a playmate.  For starters, she's generally more comfortable around males than females.  She also has a dominant, confident personality and does NOT do as well w/ another dominant dog.  She rarely gets along well w/ hyper, small, nippy dogs.  As soon as we had that info, we started looking.
 
And that's when we found Thatcher.  A 40 pound, submissive male.  We set up an initial meeting knowing that if Ponce didn't like him, all bets were off.  Oh, and this meeting?  It was on NEUTRAL ground. 
 
Well, they hit it off right away.  So well, in fact, that we took him home that very night.  We made sure to let Ponce enter our house BEFORE Thatcher.  We fed Ponce first.  And we didn't get involved when they had their little disagreements (as long as it wasn't aggressive, which it never was).  Sure enough, without an hour of arriving home, the two of them were playing in the living room and became best of friends instantly.
 
But what people are reminding you is correct.  A puppy is ALOT of work.  Thatcher was a year old when we got him.  In comparison to Ponce, he's been a TON of work.  He has an anxiety disorder (which we identified after he had been w/ us 3 months).  So, we have follow ups with an animal behaviorist.  He has anxiety meds we need to give him 3 times a day.  We've had to adjust to training him COMPLETELY differently than we trained Ponce.  He's been in our house since March and we're STILL dealing w/ housetraining accidents. In short, in comparison to Ponce he's been ALOT of work.
 
But we realized the potential that could happen going into it.  And we're willing to devote the time/money to two dogs.  Even vets appts.  We went from $200 in yearly vet expenses to $500.  And that doesn't include food, flea treatments, heart worm, treats, supplies, etc.
 
Not trying to talk you out of it.  Just reminding you to be ready.  Its double the work, but double the fun if you've got the right mindset!