What are the signs...

[Biscuit]

A little back ground first, we just recently (2 weeks ago) got another dachshund who is now 12 weeks. We have already a 3 year old dachshund.
My question is now how would the 3 year old act if he were jealous or not happy with the puppy being here?
I'm not sure what to watch for behavior wise and just want to make sure both dogs are as happy as they can be.

[amelioratione]

Some common symptoms I've read about are sluggishness, growling, sulking, snarling, fighting, and refusal to eat.

I've also seen some dogs, refuse to let the other come around "you" because they want all of your attention. If not that, when you're giving your new dog attention your other one is trying it's best to catch your attention away from the puppy - ie. whining.

[Shmee]

As kid growing up, we had a male german shepherd. When he was about 4yrs or so, we decided to bring a female shepherd puppy into the house so he would have a companion to play with. She was the cutest and abit more attentive than the male was. She lasted in our house for one week. Jigger, (the male) stopped eating and lost about 20% of his body weight in that time and wasnt overweight.
He also displayed aggression and ZERO interest in spending anytime with her, although, not because of her not trying. She wanted to play with him and all he was able to do was snarl and growl. We were never able to leave the 2 of them together because we'd always live in fear of him doing damage. Sadly, she was returned to the breeder 1 week later.
So, I would give your adult the upperhand when it comes to living with a new housemate. You really have to watch and see how they interact. You will know if he DOESN'T like her. If you've gone this far a period of time without incident, you're probably home free.

We had our male JRT 2 years before we brought Kaytee home. We were very concerned that she would not be welcome by him, but she took to him and vice-versa so, it was never an issue. They actually never fight, they'll play (very) rough sometimes, but never more than alittle squeel is heard where they both know the game is then over at that point. They know their limitations with one another and that should be the focus of your 2 dogs. I never even have a 2nd thought leaving my dogs alone together in the house and trust them (almost) implicitly to make the right "doggie choices" so all members of the house are happy.

I hope you enjoy the same experience

-Shmee

[saden99]

Usually the biggest sign of jealousy for a dog would be simply attacking the other dog. However if the 3 yr old Dachsund understands that you don't want that and he would be punished for it then he/she may be more inconspicuous about it.

Hogging attention
Being sluggish(but not lethargic)
Doesn't want to eat but still jumps for treats

I had a dog before named Max that we had rescued about a mile or so behind our house...tied up to a tree with moldy bread and no water. He was a wonderful dog and even knew a trick to play dead when you would make a "gun" with your hand and say "Bang!".

About 3 years after we rescued him we got another dog from a friend that was going to otherwise have him put in a pound. Shrooms(the new puppy) was definitely something Max was jealous about. He would tackle the poor guy, bite at him harder than he should have and really try to hog all of the attention if Shrooms ever tried walking up to anyone.

Eventually those two were great friends until something happened and they were deep seeded enemies(have absolutely no idea what happened). One day they loved each other and the next they attacked each other.

It couldn't have been jealousy because they both got the same amount of attention. Shrooms was my dog and Max was my sisters. They were both intelligent, loving, and loved to play. Perhaps it was just because they were both male, although neutered losing their you-know-whats doesn't always deal with behavior issues.

For now neither dog will be completely happy. The 3 yr old may be jealous but eventually they will both work out their issues

The best thing to do is supervise them when they are together and let them play. If things turn far to rough then get the puppy out. "Too rough" is actually quite rough for a puppy. They can take a beating since puppies usually play with their brothers/sisters when they're born and their mother teaches them many things such as how hard is too hard when they bite.

When one of them starts yelping or if the 3 yr old shows teeth, stares the puppy down and growls then you may consider a muzzle to train the dog to like the puppy.