I would like to present a some thoughts and suggestions on this scenario:
1> Your neighbour has a responsibility to keep her dog on her own property and to not let it be a nuisance to her neighbours or your birds.
2> Your description of the events that happened next day tell me the dog acted in a fearful/scared manner. It knew it should not be on your property and when it could not easily escape it has acted defensively - including biting you. This does not mean that the dog is inherently dangerous.
3> The argument has resulted because your neighbour has then also acted in fear, that you will involve the police or perhaps take some action that might result in her dog being taken away.
I Suggest -
Open a line of communication with your neighbour again, ask them to come meet with you over a cup of tea (be sure to tell them that this meeting is a peacemaking mission and make it as non threating as possible).
Explain that it is in BOTH your interests to ensure that the dog doesn't do this again.
Explain that you believe the dog acted in a defensive manner and that you do not wish to take any action against the dog 'for that one example', but that you also had a need to protect your ducks and yourselves - hence your wife holding a space.
Show her your injuries - so that she has clear evidence to show that her dog bit you - and reiterate that your combined efforts to sort this situation is required to avoid a repeat scenario.
Offer suggestions to your neighbour if you have any - can they kennel their dog until the fix hole can be fixed? Decide who's responsibility is it to fix the fence hole and/or come to an agreement as to who/how the fence will be fixed.
In future - if the dog comes back to your property - your actions should include the following:
1> Address the immediate concern - remove the ducks to a safe location.
2> Photograph/Film/Document Details
3> DO NOT aggressively chase or approach the dog. Let it retreat to a corner or under a bench then either calmly call your neighbour to retrieve her dog or call a dog control officer to remove the dog.