For the source text click/tap here: Pesachim 70
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In an attempt to clarify when and how the Paschal lamb will be sacrificed - particularly when the 14 or 15 of Nissan fall on Shabbat - the rabbis compare and contrast this offering to that of the Festival peace-offering. The rabbis disagree about many factors: which should be sacrificed first how they should be sacrificed (roasted, etc.) where they can be slaughtered etc. etc. Steinsaltz explains that one rabbi Yehuda ben Dortai moves with his son far from the Temple to physically distance himself from the rabbinical rulings about the Festival peace-offering on Shabbat - a ruling with which he vehemently disagrees.
The Talmud indicates that Shemaiah and Avtalion were not merely (Pharisaic) leaders but also heads of the Sanhedrin. In our daf a Baraitha relates that Judah ben Dortai said if Elijah were to come and reproach Israel because they did not sacrifice the Hagigah (a private sacrifice) on Sabbath, the answer would be that Shemaiah and Avtalion, great sages and great interpreters (or: preachers) did not tell Israel that the Hagigah took precedence over the Sabbath.
Why did Judah ben Dortai and his son settle in the South? Did he join the Qum-ran sect located there? Does the fact that his wife obviously did not accompany him have any significance? The sources indicate no answer to these questions.