In an effort to delay, you MAY want to agree to meet with her attorney to discuss the prospect of him representing both of you. I think they may call it collaborative divorce depending on the state.
You certainly won't be going this route but your wife and the attorney don't have to know this.
If you say "no" to this proposition today, your wife will just pay him and he'll prepare a case and file ASAP (before you do...since so many attorney's think filing first is an advantage).
If you say "I don't know, let's set up a meeting" you can prolong this process and maybe get your wife to settle down about the exposure and not bother filing. Once the affair being over sinks in...getting this divorce done ASAP won't be such a pressing issue. She'll be depressed instead and unmotivated to pursue this course of action.
Therefore, agree to meet with "her" attorney. Listen to what they have to say. Maybe even get them to document their "reasonable" position. (this could be great evidence if she later claims you are abusive or a drug addict or something and tries to take full custody of the kids as an act of vengeance). Then leave the office saying you'll think about it. Then, do nothing. Don't talk divorce and wait to see if she ever gets around to actually filing. If she does....THEN hire your own attorney.
It's also possible you could say "yes", make the attorney both of your attorneys and THEN, don't agree or sign anything. Then, I believe, that attorney can't just represent her in a separate divorce case because he was also your attorney for a brief moment. She'll have to find another attorney to file the case.
Delay. You might buy yourself a couple weeks here before she files. She's mad and being reactive. She wasn't in a hurry to file last week so maybe she'll drop the notion here in a short time once this all sinks in. Time is on your side. Drag it out.
The internet is 90% complaining and entitlement and I hate it because I deserve better!