Your situation sounds very similar to what I am going through - but without the affair part. Since my daughter was born two years ago we have had sex four times - the first instance was almost one year after she was born. Not forgetting that we didnt do anything once she found that she was pregnant. Even the four times since have not been pleasant - regimented as you aptly put. There has been other circumstances that have placed a lot of stresses on the relationship too.
We too have slowly drifted apart, but this is due more to my wife's excessive controlling behaviour. She now takes the kids to bed at 8pm and sleeps herself saying she is tired. She has started to spend most weekends doing things for herself i.E. Hairdressers, overtime at work - leaving me with the kids. Its now to the point where we find it difficult to have a conversation.
I have spent the past weeks trying to find out what I wanted out of the relationship with my wife, my kids, how my work fits in, how I see the future panning out. I wrote it all down and gave her a copy to read through. Im my case she read it and put it aside without comment. So far she has refused to discuss it - I think she has logged itas my attempt at a mid-life crisis. In my instance did not become the discussion point I thought it would (i was hoping to have her input into our life, her hopes, her dreams, her values and beliefs and make it into a family plan). However, it did clarify in my mind what I wanted to do and where I wanted to go. I was then able to plan contingencies based on certain events.
Is your wife's affair a cry for attention? (i'm not a dr so don't read too far). I think that you need to find what you want from the relationship first. Write it, plan it (call it a family mission statement if you like - all very yuppie, I know). Once you have your mind sorted, see where your wife wants to fit in.
Hang in there, it takes a little time to make the right decision. I've never found counsellors much good. However i've found this forum a refreshing change.