Legal Question in Family Law in California

California is a no fault state. The simple fact your partner cheated does not entitle you to any more or less then you would normally receive under the law. Until you have an order from the court custody will remain murky. Although I do not recommend it, custody tends to stick with the status quo as much as possible. That is because the courts solely look out for the best interest of the child. I would establish a visitation schedule and remain in the home. I would talk to an attorney in your area.