Parental rights? We were together when she was born. I signed her birth certificate and shared the same address for the first 6 years of her life.
Established paternity? I signed her birth certificate. I have never taken a paternity test, she has always been my daughter. I don't feel it's necessay to take one now its a little late.
The problem is that since you chose to have a baby without the benefits of marriage, the father does not automatically get rights. Signing the birth certificate is a start, although you'd have to check to make sure that that's sufficient in your state. (If it's not, you need to see what is required to establish paternity at this late date).
After that, you have to file for custody and/or visitation with the courts. It would be nice if she let you visit the child without a court order, but that's apparently not going to happen, so go to court and get an order for visitation, at the very least. You might also be able to get joint legal custody.
You've had 7 years and never did that, so you may have an uphill battle. When was the last time you saw the child?
She can not simply terminate parental rights without you being notified. The more recently you've been in the child's life and paying child support, the harder that is. In most cases, it's almost impossible unless the new husband adopts - but, again, they'd have to notify you. Similarly, you would have a right to objecting to her changing the child's name.
Go to court to establish visitation. If Mom has tried to terminate parental rights or tried to have new hubby adopt, then she will bring that up - and you would challenge it for lack of service.
But, ultimately, it comes down to you getting up off your couch and taking action to establish and enforce your rights.