Good afternoon and welcome to Just Answer. I would like to take this opportunity to thank you for the opportunity to help in answering your question. Furthermore, I would like to say that I am sincerely XXXXX XXXXX hear of the difficulty you're experiencing within your marriage.
Based on the detailed information that you have kindly provided it sounds as though there may be several factors in question here. It sounds as though you're wife is using her going away as "payback" for your cutting her off emotionally and physically. Despite the fact that this could have been handled better it appears to be evident that you have made multiple attempts to reconcile and have gone so far as to acknowledge that you were wrong in doing this and attempting to reconcile.
Having said that, my impression is that your wife's response may be over-exaggerated in that she goes away for the weekend and has no contact with you or the children the entire time. She likely waits for the last minute to let you know is due in part of her wanting to avoid a confrontation. I'm truly sorry that you are going through this as well as for the children to witness this behavior your wife is exhibiting...as this can't be healthy for them to see.
I recognize the fact that she says that she is no longer in love with you and is showing you disregard by just up and leaving each weekend with no contact....but I get the impression that you are willing to do whatever is necessary to save your marriage. My initial inclination is speak further with her about going to marital therapy in order to try and work out the issues that you've mentioned and to further address the original issues in relation to communicating with one another. My inclination is such that she will be resistant and I would urge you to persist and continue to request marital therapy in order to work through the problems you're both facing. Mind you, I recognize that this will be difficult for you in both the request as well as the possibility of being rejected.
My hope is that the therapy will help you both to work through your problems and resolve the issues you're confronted with. Furthermore, (and forgive my bluntness) the therapy could also help you to work toward an amicable separation. Your wife goes away each weekend without consideration for not just you but her own children which is (again forgive me) is unconsciable. You have some decisions to make with regards XXXXX XXXXX marriage and the mental health of both you and your children. I would start with the above suggestions. There are also workbooks that can be purchased with techniques to help you both work on issues in your marriage which would be a good start if she is willing to do so.
Again please accept by sincerest apologies about what you are confronting and I hope that my answer has been helpful. Please feel free to ask any further questions that you may have so that I can ensure that I have answer your question completely and thoroughly. My intent is to be certain that you are satisfied with all aspects of the answer and suggestions I've offered you. I look forward to your response and thank you again for the opportunity to help.