Change of ownership

I wonder if any of you have any legal knowledge? Trying to keep this as short as possible, I lost my two old dogs in 2013 and 2014. They were 15 and 17. My daughter's then bought me a new dog in 2014. He was nearly 2 and was being rehomed due to a change in his owners circumstances. She was devastated to let him go but, I keep in touch about 3 times a year so she knows he's well.
Last June, my daughter saw another little dog looking to be rehomed. She knows I prefer having two, they keep each other company. My son in law contacted her (text message which he's still got) and asked for details, adding that he and my daughter would like to come and see her at the weekend. The person selling confirmed that she was selling on behalf of her mother but that she had a number of other people interested and could they go that evening. They went, the dog was wonderful, the money was paid and brought home to me. The seller did say that the dogs vaccination cards etc were with her mother and she would pass our address on . They arrived a few days later.
As i am on a limited income, my dogs are registered with a local charity veterinary clinic. At that time, their lists were full so I was unable to register my new dog with them until 5 weeks ago (they would have seen her if she was ill, just not anything routine). Anyway, she was finally accepted and the vet saw her for a check up. She was booked in to be spayed and they scanned her for a microchip, which they found and gave me the number so I could do the legal change of ownership. I duly rang around the companies, found the right one and was told that I had to complete the necessary forms which could be downloaded from their website.
I have today been contacted by the vet as my dog is due to be spayed tomorrow. She said that as legal ownership has yet to be completed would i give permission for her to contact the first owner, just to confirm everything is in order. Of course I had no problem. Unfortunately, she then rang me back to say that she had spoken to the original owner who has stated that she now wants the dog back. Apparently, she is saying she gave the dog to her daughter to be looked after and she had no idea the daughter had sold her. She told the vet under no circumstances must she be spayed as she may breed from her.
The dog was born in September 2015, she was in her original home until November 15 when she was sold to this woman who then moved her on to her daughter. My daughter bought her in June 2016 so by the time she was 9 months she was on to her fourth home.
We have proof that the dog was advised for sale and, if she is now saying that she didn't know her daughter had sold her where does she think she has been for the last 10 months? Also, the vaccination records were posted to us and are in our possession.
Does anyone know if she can claim her back? I know i have gone on but I'm worried sick