Uttar Kand is considered an interpolation because some way that it's language is from a later era , the personality of Shri Ram doesn't match with previous Kands of Ramayana and the story of Ahalya is different in Uttar Kand than Bal Kand. In Bal Kand she is a partner in crime with Indra while in Uttar Kand she is a victim who was cheated by Indra.
The original manuscript when Maharishi Valmiki would have written it is obviously lost so it's impossible to actually find that which shlokas Maharishi composed at the very first time.
In Mahabharat's Ramopakhyan, the second exile of Mata Sita is not mentioned and even Agnipariksha is not there in it. Devas come and gives testimony of her purity and then Shri Ram and Mata were reunited and after that when he returns to Ayodhya, he lives happily ever after and does Ashwamedha Yajnas.
It's possible that Uttar Kand was added much later in the Valmiki Ramayana and Lava Kusha were born in palace not in jungle and second exile of Mata Sita is just someone's creative liberty and a fanfiction.
Raghuvansh by Kalidas mentions the second exile, Ananda Ramayana treats second exile as just her staying away in the Ashram but Shri Ram constantly monitors everything and knows about his sons since their birth and then after she goes back to the Earth, the Earth due to Shri Ram returns Mata Sita and she is again crowned as Queen.