That's all very tidy, but what you've described is barely in the show at all.
Until reading your comment my recollection was that she left it with her sister; apparently that's wrong and you can figure out what really happened by piecing together a few different short scenes across several seasons. As someone who watched the show as it came out over 8 years, it was like the baby fell off the face of the earth with no explanation.
The baby did fall off the face of (Peggy’s) earth. She gave it up shortly after it was born. That’s it.
As I said, it comes up again and again. Most directly in “Meditations in an Emergency”, wherein she tells Pete the whole story of his baby and why she gave it up.
Until reading your comment my recollection was that she left it with her sister; apparently that's wrong and you can figure out what really happened by piecing together a few different short scenes across several seasons. As someone who watched the show as it came out over 8 years, it was like the baby fell off the face of the earth with no explanation.