I was hoping to get a response back before giving you an answer, but I also don't want you waiting for a response.
If she has only been like this recently or after the departure of the other dog, reuniting her with another dog she has been around in the past would not be as big of an issue as rehoming her to a new family. However, if she always was vocal with another dog around when the humans left her alone, then she is likely to continue that behavior unless training is done.
Now that is called separation anxiety. I can give you lots of tips to help with separation anxiety. The first thing is to take your dog for a nice long walk before you leave, preferably 30 minutes or long. Make it a long, quick paced walk to tire your girl out.
Second is to use a low-key approach to leaving the house. Ignore your dog before you leave and after you come home for at least 5 minutes or more. If your house is like mine in the morning everyone is running around getting ready to leave. This has the dog in an excited mood and then suddenly she is alone. If this is the case, put her away from everyone, say in a bathroom until the frenzy is over.
Don't punish or shout at your dog when you come home and find she’s barked the whole time. When you do, you increase her stress level rather than reduce it.
You can provide her with small stimulating toys or toys that you can fill with treats. Kongs are good because you can put peanut butter or yogurt in the compartment and freeze it. Give it as you are leaving. If she is busy licking the treat out of the kong, she won't be vocalizing.
Sometimes leaving a TV or radio on can help a dog with this problem as well. Also remember to not reward a dog's excitement to you with petting and affection or even eye contact. You want to show hier nice calm praise when she is being calm.
The best way is to crate her. This prevents injury to the apartment and protects her as well if she is destructive as well. Another thing that might help is a DAP collar. These use a pheromone to calm a dog. See one here:
Practice putting her in the crate, leaving the house, opening the door immediately and rewarding her with a hot dog treat if she did not scratch, bite and carry one. This teaches her that you leave but come back quickly. Once she seems to not do anything when you initially leave, lengthen the time she must be quiet for you to come back in. Change the time as well. Make it 2 minutes one time and 10 mintues another, so she never knows if you are gone for an hour or gone for 2 minutes. It helps her stay calm for longer periods of time, just be sure you reward her when she is good.
Another thing that helps is to do things that might make the dog feel you are leaving and then don't such as putting on your coat or picking up your keys. Or leave without doing those things. This helps remove things that might trigger the dog to become anxious.
These should help her separation anxiety and boredom and help curb her barking. It will not be an overnight cure and will take work on your and your family’s part to be consistent in your interaction with her. Here is a site that also offers idea to combat separation anxiety.
There are many other methods available such as citronella spray collar, that will stop excessive barking.
Another option is medication, which is discussed on this site:
I would recommend rehoming with your family before a stranger though. I sincerely ***** ***** this information is helpful. If you are satisfied, please remember to rate my service by selecting the 5 stars at the top of the screen. If not, we can continue here until you are satisfied, simply use the reply box and let me know. Thank you!