Okay so the problem sounds like separation anxiety,
Firstly,
This is going to be a long. Long. Tedious process. Sorry. Welcome to doggy training!
I would advise to not put her in a crate, as they are not recommended for dogs with speration anxiety as they can and will thrash around, panic, bite the bars and break their teeth.
Doggy proof a room, kitchen is ideal, I'd advise a room without a window that faces a street purely because people walking past a window can wind up even calm dogs and if they get in the habit of barking and people walking by it makes them think "good, the stranger left because i barked, I must bark next time and they wont come close" and it's difficult to get them to stop. Hence the traditional hatred of the post man! (Scary noisy persoperson comes to house everyday, I bark and scare him off and he leaves = I protect house from scary person and must do the same next time)
Then make this room the best most fun room ever! Treats, fuss, comfy bed, toys, time consuming toys/puzzles,
Make sure puppy spends lots of time in there, with you.
Next stage, remove the build up to leaving, so all those little cues she's picking up on,
Putting on shoes/coats/keys/door opening ect ,
Practice those, but don't go out. Put your shoes on and walk up stairs, pop your coat on randomly and sit down and fuss, then she doesnt get wound up and afraid you're about to leave her.
Then when she doesn't bat an eye lid at that, practice shutting doors, randomly in the house, have someone shut the door to the room with you in there too and fuss and treat. So shut doors are not scary, they happen all day every day.
Then practice putting her in the room alone, maybe with a kong/treats scattered for distraction for 2 seconds. Literally no longer. Open the door and give a super tasty treat and praise. Then 4 seconds ECT. Build up slowly, do each stage a few Times, if she barks, ignore until she stops and immediately open the door and praise (for stopping ONLY) then go back a step and shorten the time and work on that stage.
This could take months, but a happy dog is a healthy one and annoyed neighbours can make your life a misery. Good luck to your family :) if you get stuck email a canine behaviourist and get some advice on how to move on. You could be doing the right thing at the wrong time or in a different way and just need guidance or a fresh perspective!
Also, no dog should be left for more than 4 hours alone but I totally understand people have to work! I absolutely recommend getting a dog flap and a dog walker.
My dog has both and shes very content on the days she has to be alone, she is a typical noisy breed and she doesn't peep.