Personally, I see a couple of different situations going on here and they may or may not all be related. The biggest thing is she is maturing mentally (according to your signature she's around 1.5?) and is starting to feel comfortable in your home. Has she been socialized with the dogs next door? What type of fence do you? Can she through it? If she can, you might consider making it solid so that hopefully lessen the fence fighting because it will just build up frustration.We have been trying to figure out Regen's behavior with other dogs, especially as we are considering fostering and/or adopting another dog.
She loves going to doggie daycare and the "counselors" there have never reported any issues with aggression or overly rough play. She loves going to her "home daycare" with Miikka, and after a couple of weeks of sorting out the pecking order, I think the two of them get along well and like to play (Miikka's mom would have the complete story though!).
Are you sure she loves going to daycare? I think the counselors at those places aren't the greatest at seeing when a dog is having fun vs just dealing with being there.
The strange thing is how Regen reacts to other dogs when WE (my husband and I) are around. It seems to have changed as she has become more comfortable and bonded to us. She used to love going to the dog park with me, but in the past 2 months, if we try to go, she will spend about half the time hackling and barking at other dogs who try to come too close to wherever I am.
This could be resource guarding. Does she do this in other settings too?
When we are hiking, her recall is great except in one instance where someone else had his 2 dogs off leash and she decided it was her job to "hold" them off and stood in between us and barked at them.
She does this on leash, which we have treated as reactivity and has improved with "watch me" and "look at that" as well as avoiding situations (because nobody wants to have their walk ruined by a lungeing, hackling, barking GSD!).
She never used to do this off leash with other dogs, though. When we went to meet a potential foster dog, she was barking her head off (though not hackled).
Where did this meeting take place? Was it on neutral ground? Were they brought together face to face or from the side?
In the past month, she has started running out the door to the backyard and barking/hackling at the fence to our neighbor's yard (they have dogs, too). She never did this before, and now she does it every time we let her out.
This could be maturing and her starting to "guard" or "protect" her territory. I noticed it with Raven when she was 1.5-2years old.
I am trying to figure out what is causing this behavior, and wondering how to work with it.
Things we are already doing: NILIF (sits/waits before eating, going out or in a door, getting into car, getting collar leash put on, has to do a down or something we ask before getting pets), working on "watch me" and "look at that" from a distance.
In my experience with Raven, she did alot of the same things you are mentioning when she turned 1.5 -2 years old. She stopped getting along with every dog at the dog park. She had matured and no longer liked playing with strange dogs all day long. It may be time to stop the dog park and day care. A lot of adult GSDs just don't enjoy being thrown into play with strange dogs even if they did when they were younger.