It sounds like your dog is indeed very anxious.
The answer of user14052 has the potential to solve the problem, but depending on how you interact with your dog, it could make it so much worse.
Let me explain: For the sake of simplicity I'll refer to the 7 months old dog as "Puppy" and the 3 years old as AD (anxious dog).
- "Puppy outside" is a stimulus that is connected to negative feelings. AD expresses these negative feelings by yowling.
- Eventually, Puppy comes back inside while AD is still yowling. He connects his action (yowling) with the positive outcome that Puppy returns. This is a self-amplifying behavior.
- If you talk to and pet AD while he's yowling, you actually reward his yowling, which amplifies the behavior even more.
But you could use the same mechanism to change and eventually stop the behavior in a process called "Classical conditioning". (This is actually the foundation on which any type of pet training is based.)
We already established that AD reacts to Puppy going outside alone. Fortunately, you are completely in control of when and how long AD is subjected to this stimulus.
The New Reward
You need to analyze what is the best possible reward for AD. Most dogs react best to:
- Food. Almost all dogs react positively to treats. For the training, you should choose a very special treat that smells absolutely, irresistibly delicious and he never gets outside of the training (like a hotdog wiener or cheese).
- Play. Some dogs won't accept treats when they're too excited, but a short play session is always welcome. This works best for dogs that are very focused on toys, like the typical "ball junky"
Bad choices are:
- Verbal praise. Since AD is very verbal and loud, he wouldn't perceive your praise as a reward, but probably as you joining him in his yowling.
- Petting. Most dogs love to be petted in a calm situation, but in a training situation, petting was proven to be inefficient.
The training is simple in theory, but will most likely require several weeks to change the behavior of AD.
- One person goes outside with Puppy, one stays inside with AD
- Before Puppy goes outside, you prepare the reward (get the toy or food)
- When Puppy is outside, you distract AD with the reward. Be absolutely blunt and hold it right under his nose. He must notice the reward over his own anxiety. It's absolutely vital that AD sees Puppy go outside first (his stimulus) before you introduce the reward.
- When you caught his attention, move the reward slightly away, so that AD has to turn his back to Puppy in order to get the reward. If he's too focused on Puppy, you can skip this step for the first few training sessions.
- Reward AD intensely for a long time to make this reward better than his yowling. That means: play with him enthusiastically until Puppy returns or feed him one tiny piece of treat after another to stretch it out.
If the third dog wants some of the reward as well, either share it or lock him into another room for the duration of the training if he's disrupting too much.
Eventually this will connect the stimulus of Puppy going outside with positive feelings. After a few weeks of training, you can start to decrease the reward in small increments until, eventually, you can go outside with Puppy while ignoring AD.