No, Rory and Amy had baby Melody stolen. Baby Melody was named after Amy and Rory's life long best friend. Baby Melody was brought to earth and raised in the orphanage in the second episode - where Amy saw a picture of herself with a baby - at some point in the 1960s.
Child Melody was imprisoned in the astronaut suit, but broke out of it when Amy shot at it in 1969.
Child Melody regenerated in the alley in New York.
At some point Melody regenerates into toddler Mels, by now she's in Leadworth and grows up with Amy and Rory, the three of them are best friends. And yes, I think Mels knew that they were her parents, which is why she gets Rory and Amy together as teenagers.
Mels doesn't do weddings, so she wasn't there when Amy and Rory got married, but turns up in the corn field when Amy and Rory do the crop circle. At this point, she is yet to become River Song, so tries to kill the doctor. Then she regenerates into River Song, and Amy has one of those
moments as she works out that she named baby Melody after herself.
I'm pretty sure I understood that, but someone can correct me if I've missed anything, or cocked it up.