What are the rights of a wife who has been proven to have communicated with her ex-husband and agreed with him to return to him after her divorce from her current husband?

If the wife's adultery is proven, it is permissible for her husband to pressure her so that she may free herself by returning the mahr (dowry) and expenses he paid, and by waiving her rights, such as the deferred mahr, after which he divorces her. This is based on the Almighty's saying: "And do not make difficulties for them in order to take [back] part of what you gave them, unless they commit a clear immorality." (4:19) The clear immorality includes adultery, disobedience (nushuz), and abusive language. It is permissible for the husband to take the mahr, or more or less than what he paid, based on the Almighty's saying: "And it is not lawful for you to take anything of what you have given them unless both fear that they will not be able to observe the limits of Allah. But if you fear that they will not observe the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself." (2:229)