
Hello and welcome to the forum :)
Well seems your neighbours are not the most hepful - hard to believe that the council are being so unsympathetic with a
12 weeks puppy!Anyway, firstly, were this me I'd have a chat with the neighbours and explain this is very much a temporary problem as you're trying to train a very young puppy and, like any human baby, when distressed for any reason they make a noise. Explain that you've sought advice on how to get over this temporary glitch and ask could they please be patient in the meantime :)
Onto the puppy. I don't leave pups to cry and whine - they do so because they are distressed which could be for a number of reasons. I'd suggest that you may have to set up a timetable of 'events' which are possibly better suited to your pup's immediate needs until the little mite is able to keep dry and clean overnight as well as feel secure.
1. Ensure your pup's meals are spread out well through the day. For eg. 7-30am, 12-30pm, 5-30pm and 10-30pm. Pups have very small tums which is why at this age they need 4 meals a day - they also therefore get hungry quicker and need to have meal times spread across as large a time frame as possible :)
This helps prevent your puppy crying through hunger2. Ensure puppy has toiletted fully before bedtime. Stay up if necessary later than you would normally to ensure pup is comfortable for a night's sleep. A full night's sleep for a pup of this age is anything between 4-6 hours only so set your alarm to get up BEFORE you expect the pup to wake and take it into the garden to relieve itself. Don't play with or excite the pup in any way - calmly allow it to toilet, praise of course but not too excitedly, and return pup to it's bed.
This helps prevent your puppy crying through needing the toilet or being being soiled3. And TBH, this is my main feeling here - don;t leave the puppy to be afraid or distressed on its own. If you haven't already done so, have the puppy sleep in a room with you or if not practical take up temporary residence yourself in the room the puppy sleeps :) This doesn't have to be a life long situation by any means but if your puppy is scared or feels abandoned it will cry just as loudly as one which is hungry or soiled. Build the pups confidence gradually to accept periods alone and pre-empt times when it may wake up so that you can attend to it's most basic needs without it having to holler and bring the house down :)
I'm sure with a few minor adjustments in your current regime (which TBF I can only guess at!) you will very quickly resolve the issues with your neighbours and, importantly, have a routine that works best for the puppy and your family so peace is restored for all.
HTH, best wishes Teri