allen, i am in the EXACT same circumstance, no divorce, 1 yr of praying & pleading, kids, my wife lives with her new man with our children. if fully understand your desire to quit..i wrote a long post for you and erased the whole thing. i stopped and prayed and asked god, "god what do i tell someone to help them, when i dont have the answer either?" and back came "WAIT"
allen, i am not one to ever say 'God told me' because i am never sure whether he really did..but i can tell you that i was still arguing with god about telling someone to wait when i dont know them or what has happened and while still arguing with him i flipped my bible open and this was the verse that jumped off the page...ps 37:34 "Wait on the lord and keep his way. He will exalt you to inherit the land; When the wicked are cut off, you will see it"
So allen you will have to draw your own conclusions but i take that as a clear directive from your heavenly father to tell you to WAIT! I know it is hard, but you should probably pray alot about it...before you give up i would like you to know there are many here on this site who are "standers" they are people like you and i who are praying for our wayward mates..for god to get a hold of them and turn them back to gods plan for their lives..there is also a website for standers.
www.rejoiceministries.com please check it out before you give up.....
Lord i pray for ###, i pray you will show him your will and direction for his life...lord please reach his wife and flip her around, set her straight.pour out your plan and purpose and will for her life..pour it out where she cant miss it, lord reach this wife in whatever way you must to reach her, soften her towards ###, towards you, towards her kids, towards her marriage..lord if you are saying "wait" you must have a plan and your plans can never be thwarted..in fact only your plan will last. so lord bring your plan to this home and bring it to pass swiftly i pray in jesus name amen...