Here are my thoughts:
The OP, for some reason, must have been certain that her kids were responsible for the damage because she immediately agreed to pay for the repairs.
I don't care what, if any consequences, the Op's kids suffered. They are her kids, and her problem.
If there is a hole in your window that was caused when a BB was shot through it, the window has been "shot out." I don't care if it is a hole the size of the BB or if the whole window was shattered, I am not living with holes in my window even if the damage is minimal. Especially if me or mine didn't cause the damage.
I have a very hard time believing that 3 broken windows were an "accident." one? yes, after that, not so much.
These children need more supervision when using these BB guns.
The OP is VERY, VERY lucky the only thing that was damaged was windows. Had her children shot the neighbor, or the neighbor's pet, or dog forbid one of the neighbor's children, this would be a VASTLY different situation.
It would have been nice had the neighbor gotten more estimates, but she was under no obligation to do so. The neighbor was also under no obligation to allow the OP to get estimates.
The neighbor is perfectly within her right to choose a licensed, bonded contractor who is knowledgeable about the type of windows being fixed.
The neighbor has the right to have her windows replaced with windows of the same quality as the rest of her house. She should not settle for cheap, contractor grade windows to save the OP a buck.
Again, I do have the "crazy" Pella windows. I can't even find a price to replace the glass on the internet. It seems the only way you can get an estimate is to have a Pella authorized contractor come to the house. I think, all things considered, the OP got off very cheaply at $450.