hello myrab51
Welcome to the forum.
The other day I happened to be reading an article in W.V. Cats.com that I think sounds like it could shed some light on your problem. I don't think the new kitty is being vicious, she's perhaps trying to play with the dog. The problem is that without having any siblings or mother, it would appear that she has not learned the art of playing without being rough.
I'm including a web site and the article is in 2 sections, so I'll include them both. Something else I found with this site, there has been quite an amount of investigation done. You need to go down the menu on the left hand side and click on "Links related to Cats". It is full of information that could be of value to you.
http://www.wvcats.com/biting_cat.htm
http://wvcats.com/bitingcatplayaggression.html