I hate to say it but I think your wife is behaving in a completely irresponsible way and she's splitting up your family for a god that no one has ever seen, she should allow the children to find their own beliefs in life and stop influencing them.

I have a family separation situation, initiated by myself though. As I started openly expressing my disinterest in religion, the criticism from my mother and family members was becoming harsher. There is precedent for it in my family, so rather than coming out as an atheist and being ostracized, I cut off all contact with my mom. I have come out to my sister since, but actual conversation with her has become nigh impossible because every message from her is about returning to the faith.
As other family members started applying social and emotional pressure on me to reconnect, I cut them off too. None of them save my sister know I've turned atheist, but if they did they would have been much harsher and not be speaking to me in the first place, as my sister has threatened to do since I came out to her. Come to think of it, we haven't spoken since.

I'm surprised my sister let's me talk to her teenage kids though. At least she trusts me not to "corrupt" them with godlessness. Atheists not having any morals and such. My 2 nephs and a couple cousins my age are the only family I have right now.

My kids mother is a staunch literal conservative christian, so every word in bible is true and divinely inspired by God. I am lucky that she still wants me to be a part of their lives so I get to spend time with them normally about a day a week. I can see the influence that religion has over them but I am pretty sure that as they go through their teens I will be able to act as a counter balance against that dogma. I don't mind if they turn out religious, as I was for the first 40 years of my life, but I want them to know that non-belief is a real option, the saner option, so that they are not angry and confused when they finally realize that religion is a con game in their later years.

Way, way back in 2008, I was "unfriended" on FB by my 2 nieces (whom I adored) because of my anti-religious stance. Since then, I'm pretty much persona non grata to most of my family. The loss of my very close relationship with my brother is the most painful. My mother has finally decided to put up with me, sorta...there are days, like today, that it all comes washing over me and sends me into depression. The thing is, after almost a decade of seeing how easily dismissed I was from their lives, I wouldn't want them back in mine - even if offered. I believe that I've seen their true selves...but it can still be very sad. I'm very thankful for my children and husband who have stood by me while I grieved.

I haven't experienced it but I do sympathize with you. Would she rather you pretend to believe so you could see your kids? It's a mystery to me how believers will behave.