You can't stop her from getting the D if that is what she wants, so it is fruitless to try. That said, you can certainly let her take on all the work for it. Mediation is a much cheaper and possibly less contentious environment than battling it out in the courts. Some people refuse and hold out for the courts because that process can take longer and buy them more time. Personally, I would prefer to do mediation. Of course going to mediation does NOT mean that you have to agree to her all of her demands, or even agree to what the mediator says. You can go in and walk away at any point if you are unhappy with the process.
I don't understand why you won't discuss financial arrangements with her so long as she is with OM. That makes sense for discussing the relationship or possible R, but the financial stuff will have to be settled at some point. It seems like you are using that as a threat to try to get her to stop seeing OM. That is controlling. Stop trying to control her. If you want to just wait for her to file and deal with it all then, that is fine, but you will have to deal with the financials whether or not she is still with OM.
I hear you about the house. I am in a similar situation. I would just give it time and see how it plays out. If it ends up that you want to move out there is no problem. If you want to stay you can cross that bridge when you come to it. I don't think there is anything you can do right now to help that situation.
W 34 Me 42 Married 7 years together 8 0 kids 1 beloved dog BD 4/6/2018 I moved out 4/7/2018 I moved back in alone 8/05/2018 I file 3/06/2019 D official 5/7/2019