No Custody Agreement When Leaving Home

If my wife and I agree to everything in a separation agreement except for custody and we both are moving to new residences, at least I know for a fact I am, who does my child stay with? Can she just put him in the car one day and take him to her new residence across town? For that matter can I do the same?

Yes, either of you can take the children without permission of the other. As long as you have no formal custody arrangement in place, either parent has the ability to take 100% custody of the child. I would not advise you to do that however, since she would likely then file for custody and allege that you are withholding the children from her without cause. This would not reflect well upon you in court. If she does this, then you should file for custody immediately. The best thing to do before this happens is to prepare a custody agreement with each other.