I am not going to side with you. I think the way you describe things, and because many are dog owners, it's real easy to get a lot of sympathy here on this bb. And I think you are in the wrong. I think people often go to a bb to get sympathy and to get their idea reinforced and their indignation confirmed, and there are always many people who will go along with them. I think it's very counter productive in many cases.
I think you need to be a lot tougher on your dogs about their barking, and there is nothing that says a dog has to go out late at night. Feed them in the morning instead of at night so they don't have to go out late, and take their water up at 8 pm unless it's very hot. At 10 put them in their crates and leave them there. They will get used to it if you stick to it.
I would be furious if my neighbor had three dogs that barked 'only four times' when I was trying to sleep. Your homes are too close together. Working people need their sleep. The neighbor isn't showing any indication that she's 'stressed', she is just angry. And even if she was stressed, that wouldn't be a valid excuse for being inconsiderate. All the more reason to try and help her out.
In other words, if she has become 'strange neighbor' what has gotten it to that point? Your actions. Never avoid responsibility for how other people respond to you. Think about how you can make it better.
You do not need to take your dogs out after 11 pm. A dog can get used to ANY routine. It is all in whether the owner is willing to cooperate and adjust their schedule to get along with their neighbors or not.
It doesn't matter if you have happened to hear her screaming at people and having argument in her house. I had a REAL loud screaming argument with my boyfriend when he took my dog out for a walk, let go the leash, and it got hit by a car and killed, as well as when he let a cat into the house that killed my canary. You don't have any right to try to find a way to blame her for this problem. This is your problem.
Neighbors are important. You and your neighbors need to stick together. To get along with them requires compromise and give and take and accomondation. And to get along with your neighbor, you can get your dogs to bed earlier and keep them quiet at night. It isn't your right to bother people with your dogs, no matter WHAT any other irresponsible things neighbors do with their dogs.
Be a responsible, cooperative, and flexible dog owner.
Send the lady a note, 'We have discussed our dogs schedule with a professional trainer and asked him for ideas. We've changed our routine so our dogs will be quiet at night and we won't have to take them out later. We'll work very hard on this problem. To peaceful evenings and good friends, Your neighbors'