OMG, I am struggling to believe that so many Mumsnetters are siding with the OP, and not the child. The child is apparently a little girl of approximately 5 or 6 years old, and all she is doing is looking over her fence, and watching the dog, and the OP too when she is out there as well.
The little girl is not constantly kicking a ball against a wall, or the fence, neither is she running around her garden screaming, so I genuinely don't know what your problem is @lilybit2025?
How about - as you are supposed to be the adult in this scenario - you either train your dog to not bark at the little girl, or you put your dog back indoors when she comes out? Even better, how about taking your dog for a nice walk, where it can use up some of it's boredom by having lots of great new smells to entertain and stimulate it.
The overall picture I have in my mind is: two adjoining gardens, one where a dog is left out in it so that it's boredom doesn't annoy it's grumpy owner, and the other garden where a perhaps - not coping too well with life at the moment - mum, lets her young child outside, in a safe place, but on her own, for too long a time, which will obviously have a negative effect on the little girl, maybe of boredom, and/or loneliness, but hopefully not as severe as neglect?
In your place OP, I would have chatted to the sweet little girl, and told my dog to stop barking, and then I would have tried to get the dog and the little girl to interact together! Oh, and there is no way that a five year old's behaviour at just looking over her garden fence is in anyway rude. I think that the OP is the one being rude here...