Generally I agree with you about the money, however it appears his mistress wants a Catholic wedding. Personally I don't believe that he cares one way or the other about a church wedding, but she does.
The local bishop needs to make a statement that lets her know a church wedding won't happen!
It doesn't matter. If a bishop violates canon law (if it is indeed a violation of canon law, which it seems to be), the sacrament would be invalid. Society may see them as married in the Church, but the eternal reality is that they are not.
I don't think having the Bishop make a statement would make a difference either way...