UGGGGGHHHHH! I'm in a dilemma-It's a dog day afternoon.

So last night our neighbor calls & says that her dog is almost dead and our dog did it. My husband went over there and she told him she knew it was our dog and that she's not working so she would like him to pay 1/2 the vet bill. Now I admit that our dog gets out of the yard and goes to her house and her dogs get out of their yard & come to our house. They have always just played with each other-no problems. Our dog has been missing for 2 days. We have looked everywhere for him, even animal control and he is nowhere to be found. While she took her dog to the vet we were scouring the neighborhood once again and we saw a black lab in her yard harassing her dogs. We asked her neighbor across the street if she had seen our dog and she said no but she had just seen the black lab coming out of our neighbors yard. Let me say that when her dog was attacked she was out of town and didn't see the attack. She is just assuming it is our dog. She told my husband that our dog was fighting with her dog once when he was down there and had her dog by the throat (this is where her dog's injuries are). She called us from the vet and asked for our credit card number to put a deposit on the vet bill. My husband told her that he wouldn't give her any money until we were sure it was our dog and that while she was at the vet we had witnessed the black lab harassing her dogs. She stated that the black lab was always over there and that at one point our dog had tried to fight her dog and her grand-baby was in the middle so she had to throw water on our dog. As we were looking for our dog all of the other neighbors we spoke to said that our dog is very friendly with their dogs and he has never been vicious. This neighbor & I have known each other for a while. We are not close just friendly when we see each other. Our daughters know each other and last week my daughter said they were laughing about how our dogs go to each others houses to play with each other. Now it seems to me that if our dog is as vicious as she claims shouldn't she have contacted us when she claims he had her dog by the throat and especially when her grand-baby was in the middle of an attack? Also, if she knows our dog goes to her house and he is as vicious as she claims wouldn't she have asked us to make sure he didn't go to her house while she was out of town since her dogs would be outside with no-one to "help" them? Our dogs play together in each others yards all the time. We never have problems when her dogs are here. Now I should tell you that our dog is part pit bull, part lab. He is very friendly and the most he ever does is jump up & lick people. I am not saying that it wasn't him. Just like my neighbor, I don't know if it was or not. I don't believe it was, but my opinion is biased. The thing is, she wants us to pay part of the bill without knowing if it was our dog or not. If I were rich I would pay her whole damn bill whether it was our dog or not, and if I was sure it was my Dino I would fork over the money, no problem. I'm not sure what to do. I don't know if she's blaming my dog because he's part pitt since she didn't see the incident. Pitt bull's get a bad rap. Everyone just assumes that they are nasty. Our dog has been raised in a loving environment. We have a four year old that plays with him all the time. I should also tell you that we live in the country where there are wild animals. How does she know it wasn't something else? So my dilemma is what to do. If it proves to be our dog we will pay, but I feel like she is pinning it on our dog without fact. She doesn't have money for the vet but she had to take care of her dog. Our dog is nowhere to be found, which has never happened before. I am wondering if it could have been a mountain lion since we can't find Dino anywhere. I am so worried about him and want to find him, but she just keeps asking for 1/2 the bill without any concern that Dino is missing. Now, even if it were Dino shouldn't she pay the bill & then we pay half? She actually called from the vet and asked for our cc number for the deposit. I feel like she is broke and needs someone to pay for the vet so she is pinning it on our dog. I am torn because if it was our dog we want to do the right thing the right way. We would never give our credit card number to her or anyone else, for that matter. That just isn't smart. If it wasn't our dog why should we have to pay 1/2 the vet bill. We are at a loss. We feel bad for both dogs. We want our dog back. She said that her dog will be fine, but has to stay at the vet for a few days and expects us to pay 1/2 of all costs. Are we being unreasonable? Dino has been missing for 2 days and she returned home yesterday but didn't find her dog's injuries until last night. Any suggestions/opinions?