Sorry to hear about your problem. There are few things worse than crazy neighbors. Based on your recital of the facts she was wrong. She should have communicated with you in a rational fashion. I.E. knocking on the front door or ringing the door bell, perhaps a phone call. Of course years of experience suggest to me that her version of events will be that she tried those things and didn't get a response. It becomes a a case of your word versus hers.
So the idea that you might make a claim for the emotional distress she caused you is interesting but not likely to be availing.
Keep in mind that her conduct might be legal if she reasonably presumed that there was an serious risk of injury or person or property, if she didn't succeed in communicating with you.
Of course breaking the hinges is wrong in any case, but I wonder if the repair cost is worth pursuing.
I suggest that you let her know how upsetting her behavior was while making sure she has phone numbers to reach you if in the future she discovers your dogs in your yard. That would be better than having her call animal control.
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She has no right to come into your home uninvited unless she has been allowed to do so in the past creating a license or privilege through your accepted course of conduct. If this is the case you must re-establish boundaries by giving notice this is no longer allowed.
Even if she has a right to some on the property wither by established precedent or the "emergency doctrine," ie. getting help for your "dangerous dogs," she is still liable for any damage done while on the premises (Ploof Vs. Putnam, an old VT case) You too for damage done by the dogs!
If she had no right at all (and the emergency doctrine doesn't apply) you can have her arrested for trespass. Breaking and entering etc., probably won't apply under these circumstances.
If I were you I'd talk to her, tell her you're sorry about the dogs and tell her she must not charge into your house again, tell her you were naked moments before, she should get the idea. Re-establish boundaries and FIX the fence, which ultimately makes for good neighbors.