You do not have a legal right to ask this until you get a court order preventing him from so doing. My suggestion is to immediately seek counsel and move now. Do not wait until the end of the month. Get a legal separation and have a temporary restraining order motion filed immediately to prevent him from introducing the children to someone new and to prevent him from taking the children on an overnight. Start investigating and researching this woman and if you find anything particularly curious or scary about her, place that in your motion so the court understands you are trying to protect your children.