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I would like to help you with your question.
I am sorry this has happened and I do understand how painful this is. You wrote that you had a couple of arguments. Can you tell me what these were about? Has everything been good up to this point? Did she threaten to leave before these arguments occurred...or was this totally new?
Have the two of you considered couple's counseling? That certainly might be a way to clear the air and take a hard look at what has happened. A two year relationship is not something to be thrown away without putting some real effort in to discovering what the real issues are and trying to mend them.
I can understand why you have been giving her space. That's probably a good thing given how abruptly she left. I can also understand why she is protective of the children. That is an important consideration. However, moving them to their father's house only to leave again could be very confusing for them. In addition, they likely had no opportunity to say good-bye to you and, like you, they would need some closure.
It is strange that she took the children's clothes, but not her own. Do you have any sense of why she did that? Or what she intends to do?
I await your reply.