Your sources are incorrect. The Mahasanghika is not the oldest Vinaya. In fact, it is relatively younger than most, and has been subject to a late reorganization, with the narrative contents removed and the Khandhaka completely reorganized. Moreover, the language that it uses, Hybrid Sanskrit, is late compared to Pali.
This is also incorrect. The Mahasanghika Vinaya, like all the canonical Vinayas, ends with the resolution of the conflict at the end of the Second Council.
You seem to be referring to the Śāripūtraparipṛcchā, a late Mahasanghika treatise that deals with some Vinaya matters, and which contains an account of the schism. It sets the schism at around a century after Ashoka.
Had nothing to do with schism. Non-Buddhists had infiltrated the Sangha in search of gains, and were expelled. Schism is when two separate groups of Buddhists hold a separate uposatha to establish independent communities. This happened at neither the Second nor the Third council.
Nothing at the account of the Third Council mentions the existence of different schools or the occurrence of schism. It is true that the account of the Third Council is found only in Sri Lankan sources (the Vinaya commentary Samantapasadika and the Chinese translation from similar sources, Sudassanavinayavibhasa). But the missions activity that is undertaken at the end of the Council was a genuine historical fact, and is supported directly by archeology and indirectly in other texts. This was the act of a strong and unified Sangha in helping spread Dhamma across greater India.
Yeah, this is the Śāripūtraparipṛcchā, not the canonical Vinaya.
Thus proving that some scholars will really just say anything. A difference of opinion is not a schism.
Since it has come up a few times, here is the account in the Śāripūtraparipṛcchā. Once more, this is not a Vinaya text, but a Mahasanghika treatise. It is set up as a legendary narrative, where a conversation is imagined between the Buddha and Sariputta about how things will be many centuries in the future, i.e. when the text was written, i.e. perhaps 400 years after the Buddha. This puts it about 200 years after the Second Council, and about 600 years before the Dipavamsa. (All numbers are very approximate!). I add some comments.
After I enter Parinibbana, Mahākassapa and the others should unite, so the bhikkhus and bhikkhunis can take them as their great refuge, just as [now they take] me, not different. Kassapa hands over to Ānanda. Ānanda hands over to Majjhantika. Majjhantika hands over to Śāṇavāsin. Śāṇavāsin hands over to Upagupta.
This is the standard lineage of the Dhamma according to the northern schools, accepted also by the Sarvastivada. Note that Śāṇavāsin was at the Second Council, which has come and gone long ago with no mention of schism.
‘After Upagupta there is the Mauryan king Aśoka, a magnificent upholder of the Sutta-Vinaya in the world. His grandson is called Puṣyamitra. He acceeds to the throne …
Following is related the story of Puṣyamitra’s devastating suppression of Buddhism, as translated in Lamotte, History of Indian Buddhism, pp. 389–390. Five hundred arahants were instructed by the Buddha not to enter Nibbana, but to stay in the human realm to protect the Dharma. When Puṣyamitra wanted to burn the texts of Sutta-Vinaya, Maitreya saved them and hid them in Tusita heaven.
‘That next king’s nature is very good. Maitreya Bodhisattva creates 300 youths by transformation, who come down to the human realm to seek the Buddha’s path. Following the 500 arahants’ Dhamma instruction, men and women in this king’s land again together take the going forth. Thus the bhikkhus and bhikkhunis return and thrive. The arahants go to the heaven realm and bring the Suttas and Vinaya back to the human realm.
We are not dealing with a strictly historical account.
‘At that time there is a bhikkhu called *Bahuśruta, who consults the arahants and the king, seeking to construct a pavilion for my Sutta-Vinaya, making a centre for educating those with problems.
‘At that time there is an elder bhikkhu who desires fame, always anxious to argue his own thesis. He edits my Vinaya, making additions and expansions. The one established by Kassapa is called the ‘Mahāsaṅghikavinaya’. Taking [other material] from outside and rearranging this with the remainder [of the original text], the beginners are deceived. They form separate parties, each discussing what was right and wrong.
Here the origin of the dispute is ascribed to the redaction of Vinaya. It is important to distinguish this from the Second Council, where everyone agreed on the text, but disagreed on the implementation. This agrees with the Dipavamsa, which also ascribed the split to textual redaction.
Given the timing and location of this in the north, it seems plausible to identify the textual expansion of the Vinaya with the Mulasarvastivada, who did indeed add much new material at this time. The Mahasanghika, also around the same time, removed narrative material and slimmed down their Vinaya, keeping the narratives in the Mahavastu, which is a life of the Buddha that is only nominally a Vinaya text. Traces of the former narratives remain within the Mahasanghika Vinaya, which show they have been removed.
‘At that time there is a bhikkhu who seeks the king’s judgement. The king gathers the two sections and prepares black and white tally sticks. He announces to the assembly: “If you prefer the old Vinaya, take a black stick. If you prefer the new Vinaya, take a white stick.” At that time, those taking the black stick number 10 000, while only 100 take the white stick. The king considered that all [represented] the Buddha’s words, but since their preferences differ they should not share a common dwelling. The majority who train in the old [Vinaya] are accordingly called the ‘Mahāsaṅghika’. The minority who train in the new [Vinaya] are the Elders, so they are called the ‘Sthaviras’. Also, Sthavira is made, the Sthavira school.
Note that the procedure itself is against the Vinaya. A king doesn’t get to run Vinaya procedures, and such momentous decisions can only be made by consensus, not majority. The events as described do not constitute a schism, and the text does not describe it as a schism. That requires two groups holding a separate uposatha in the same sima, with one of the groups aiming at splitting the Sangha by promoting what is not Dhamma. None of this takes place. Rather, the king thinks that monks with different redactions would be better off in separate monasteries. Kings can’t create schisms.