[Maximo]

You are wonderful for giving this girl a good home. Glad to hear that her surgery went well and that she is healthy today.

Did she accept strangers/other people during the year between when you adopted her and her surgery?

Sounds like she is guarding you, her family. Maybe she is afraid of losing her new home. How are the people approaching her? Often people are more at fault than the dog. I have problems with my Teddy because people fly at him and act like they are going to scoop him up. Or they extend their hands over the top of his head. These are all inappropriate ways to greet a dog.

If you have friends and neighbors who are willing to help, enlist them for some training exercises. You can start with having them throw her treats from a distance while you are out walking. Have them move closer and closer as your dog appears comfortable. Do the exercises without your other dog present.

I would strongly advise against the nose tapping. This only teaches your dog to associate other people with being hit on the nose. Stick to positive reinforcement and I believe you will achieve better results.

You may also want to look into clicker training and a class to practice social skills.