Problems with pronouns (ambiguity)

Mary likes John a lot, but Cindy doesn't. She(Cindy) doesn't allow him to talk to her(Cindy), because she(Cindy) thinks he is annoying.

Although the pronouns in bold are intended to refer back to Cindy--not to Mary--it seems to me (and it might just be my impression) that the sentence sounds a bit ambiguous, since either of the pronouns in question could be interpreted as if they were referring back to Mary instead of Cindy, couldn't they? For example:

1. Mary likes John a lot, but Cindy doesn't. She(Cindy) doesn't allow him to talk to her(Mary), because she(Cindy) thinks he is annoying.


2. Mary likes John a lot, but Cindy doesn't. She(Mary) doesn't allow him to talk to her(Cindy), because she(Cindy) thinks he is annoying.

If the pronouns in bold in the example do sound ambiguous, how can I rewrite the sentence to make it clear that I'm talking about Cindy instead of Mary?

By the way, would examples 1 and 2 make sense if I replaced her with Mary in 1 and She with Mary and her with Cindy in 2?