[Advaita-l] Did Shri Rama really abandon Sita?

[Aditya Kumar]

 Namaste,
A little off-topic. I have heard many people say that Ramayana ends with Shri Rama coming back to Ayodhya, united with Sita. There are many other books/Puranas where Ramayana is recited briefly. All of those accounts end with Rama uniting with Sita. However, the more recent versions end with Shri Rama abandoning Sita because some woodcutter said something. It is strange because Sita had underwent Agnipariksha right after Rama slays Ravana. Rama clarifies that, he put her into agni-pariksha although he knew she was chaste, so that people may know about her devotion and to clear her name. 
Was Shri Rama, the maryada purushottama abandon his dharma-patni because some random woodcutter gossiped about her? Even common folk won't do such a thing. It is strange. I feel like this woodcutter story was added later to undermine/insult Rama/faith in Rama.
Any leads or opinions on this matter?