I disagree with the “she has replaced you with the kids” interpretation. We don’t have enough information to say that. It sounds to me like OP is trying to minimize the impact that his overnight solo trip has on his family. He has absented himself from his children and is offering them a moment of FaceTime with some random dogs to be taken at his convenience. That is insulting.

They’re being passive aggressive about communicating hurt feelings, which is a problem, but I think OP just needs to start acknowledging the hurt feelings.