First off deep breath and steady. My husband has been yanked around more times than I can count over custody matters with his daughter. It is always stressful and rattling. Shared custody is a tough thing even at the best of times.
The words of wisdom I have heard from attorneys on these matters is the courts like to maintain status quo. In the state of Texas they prefer moms to be the main residence unless there are extreme circumstances or agreeing parties to the contrary. Finally his allegations about your dating habits have no weight if you haven't done anything in the past nine years to indicate otherwise. Remember he's going to have to prove his case. If your daughter isn't wanting to move in with him and you are happy with how things are, then his serving you papers isn't the death sentence it feels like. Your marital status is not what is at stake. The crux of the matter will boil down to two things -what does your daughter want because she is at the age where she gets a say and what kind of daily home life do you provide (safe, stable, loving, etc.). Good luck and don't panic. Focus on the outcome you want and work with a capable attorney to get there.