I'm currently living apart from my husband, as I'm an American (of Indian ethnicity) and he lives in India. He'll hopefully be here in January after his visa gets processed. It's been really tough on our marriage to be apart for so long (as we've already been apart for 6 months now since our wedding). We often have arguments, and a lot of the arguments seem to stem from the distance. When we are upset, we don't have the means of hugging or comforting each other to make one another feel better.
When you are in a long-distance marriage, communication is absolutely vital to the relationship. Make sure you are able to talk about your feelings and frustrations with the other person, else the emotional connection can get easily weakened. It also sounds like you have some sort of negative feelings to your wife for choosing to live with your children. I agree that spouses should live together. I hope you both can work through this, as physical distance in marriage should be kept to the minimal, with an end time in mind. It would be important for you both to discuss how long this separation would be, and when you both are getting back together.