Oldtimer and Starksy hit the nail on the head. They have shared true words of wisdom with you. I completely agree with them and strongly encourage you take their advice as you begin piecing. It can save you and your wife a lot of heartache and failed attempts at saving your marriage.
In my case, true reconciliation after infidelity was not possible without complete transparency in our marriage and absolutely NO contact in any form with ow. It took me three years and two failed attempts at reconciling my marriage to learn this lesson. My husband, too, made excuses for his need to communicate with ow, and when those excuses didn't fly with me, he just went behind my back. When I would discover they had been in contact (and it didn't matter to me what form it was in; anything at all was too much), any trust that had been restored was again destroyed. It was obvious he wasn't ready to do whatever it took to save our marriage. When I made it clear to him that I couldn't trust him and be in a marriage filled with secrets and deceit, my husband once again filed for divorce a year ago and moved out last summer. It was then that I established my own firm boundary that I would not even consider reconciling with him again (if he were to show interest) without total transparency and no contact with ow. When he did come back asking for another chance, I immediately made my boundaries clear to him. I do not use the transparency boundary to snoop or check up on him; on the contrary, because we do have transparency I don't feel the need to do these things. We are 8 months into piecing/reconciling, and I can honestly say this is the happiest we have been together in several years. Respect, honesty, friendship and LOVE has returned to our marriage. A little more trust is earned with each day. We are finally getting it right, but it has taken a lot of work as well as commitment to honoring our boundaries. I cannot express how worth it it has been to both of us.
What is your marriage and family worth to you? More than your current job? More than anything? Then do what it takes to honor your marriage and family and make things right. And I don't care if the need for communication is for work reasons; this woman needs to be history from your life PERIOD. If that means you need to find a new job, I'd start the search NOW.
Do everything it takes to make things right IF you indeed want to save this marriage.