My wife and I are in a kind of quasi-separation that is likely to lead to divorce. She has been and is emotionally abusive (the silent treatment, projection and gaslighting being what she does most), as I've detailed of other posts. She and the children live in a different city from me and I visit for two days of every week. For the last year I've been staying in a small separate place nearby when coming to their city, and the children have been coming to me. We were supposed to be working on the marriage but for the last four months my wife has gone back to full blown abusive behaviour and we're most likely going to end in a divorce.
My wife always used to use "my" to refer to everything that was ours (my children, my house, my money, etc.) but in the last few months has shifted ot using "our" - but excluding me. "Our" here refers to only herself and the kids. The kids have picked up on this language, so now her house is "our house", her parents (who live nearby) and relatives are "our family", her possessions are "ours" etc. The aim here seems to have been a passive aggressive method to get the kids to see my place as not theirs, and in that she has partly succeeded.
But it's also had the knock on effect of increasing leaving me out of any sense of family. How should I respond to this? A few times I've gently corrected my daughter when she referred to "our family" by saying, I'm also your family, you know, and she's then corrected by talking about "mom's family." But I don't want to keep correcting her. What else can I do?
NB: We have two kids, a daughter who is nine and a son who is about to turn five.
NB(squared): Just for clarity, I'm not asking for suggestions on how to handle my wife, but suggestions on what to tell my children.