I guess my question is, do I have any legal rights or will I lose in court?
I'm wondering what you mean by "lose in court"? By your account, everything you are currently doing is pretty close to the same as if a court had ordered it.
As other's have said, you have the right to a relationship with your child, and an obligation to support.
IMO, the mother seeking court orders on these issues' is a prudent measure for your child. I don't see why your so worried, there might be some more structured guidelines' set by the court.
I'm sure you will easily adjust, because you have been supportive, and have a relationship with the child. Look at it this way, now it's going to be "official".
Each state has it's own guidelines' and statutes regarding CS. It might even work to your advantage that she filed in her new state.
The court will use the State's Child Support Guidelines' to determine your share of Child Support.
I'm not a lawyer. This is only my opinion /suggestion. Most Replys' are based on information provided by the "original post" (OP).