As far as I am aware, as long as you are living alone with the child you qualify for the Single Parent Tax credit, and if your ex has the child for a time also he will also qualify. As long as you can prove you no longer live toegther I do not think it is an issue.
Just a note as this caught me out; If you are getting TRS as a coupld in the home be aware that the person who moved out will looser there TRS on the mortgage. A you dont qualify for TRS if you do not live in the home.