In the beginning of Mishnah Berakhot, we come across a scene in which Rabban Gamaliel’s sons return home past midnight from a night out drinking. Who are his sons? One son that is not uncommon in the Mishnah nor the Tosefta is Rabban Shimon ben Gamaliel. However who are his other sons?
It is unclear to me how many sons Rabban Gamaliel had, but we come across four different halakhic travelling experiences of two of his other sons in the Tosefta, Hillel and Yehudah:
1) Tosefta Shabbat 7:17 (Zuckermandel p118; Lieberman p28):
מעשה ביהודה והילל בניו של רבן גמליאל שנכנסו לכבול והמשיכו אנשי העיר לפניהם בצנורות יין ושמן
It happened with Yehudah and Hillel, sons of Rabban Gamaliel, that they entered into Kabbul. The people of the town led wine and oil through pipes in front of them.
In the directly previous text, we read that “ממשיכין יין ושמן בצנורות לפני חתנים [ולפני כלות] ולא מדרכי האמורי” – leading wine and oil through pipes in front of brides and grooms is not considered to be amongst forbidden Amorite practices. In this instance, we see that these two sons of Rabban Gamaliel had this happen to them and, according to this text, did not protest, nor have any issue with this practice (although it’s unclear why the previous text specifies brides and grooms, whereas our text simply has these two sons being ceremoniously welcomed in such a fashion).
2) Tosefta Ohalot 16:12 (Zuckermandel p614):
מעשה ביהודה והלל אחיו בניו של רבן גמליאל שהיו מהלכים בתחום עוני מצאו אדם אחד שנפחת קברו בתוך שדהו אמר לו לקט עצם עצם והכל טהור
It happened with Yehudah and Hillel, sons of Rabban Gamaliel, who were walking along the outskirts of ‘Oni. A man found them, whose grave opened into his field. They said to him, “One gathers bone by bone, and all is clean.”
This story of Hillel and Yehudah, Rabban Gamaliel’s sons, is presented following “מי שנפחת קברו בתוך שדהו אומרים לו מלקט עצם עצם והכל טהור” – “One who opens a grave amidst his field, say to him, ‘Gather bone by bone and everything is pure'” – which seems to show that they knew of this halakhah, while this man on the outskirts of ‘Oni did not know this halakhah (perhaps he was unsure). In their telling him this, it seemed to help put him at ease and help him take care of this situation.
3) Tosefta Moed Katan 2:15 (Zuckermandel p231; Lieberman p372):
מעשה ביהודה והלל בניו של רבן גמליאל שנכנסו לרחוץ בכבול אמרו להם לא [היו] נוהגין להיות רוחצין שני אחין כאחד [לא רצו] לומר להם מותרין אתם אלא נכנסו ורחצו זה אחר זה
It happened with Yehudah and Hillel, sons of Rabban Gamaliel, that they went in to take a bath in Kabbul. They said to them, “We are not accustomed to have two brothers take a bath together.” They did not want to say, “You are permitted to do so.” So they went in and took a bath one after the other.
4) Tosefta Moed Katan 2:16 (Zuckermandel p231; Lieberman p372):
שוב מעשה ביהודה והלל בניו של רבן גמליאל שהיו יוצאין בקורדקיסין של זהב בשבת בבירי אמרו להם לא היו נוהגין כן להיות יוצאין בקורדקיסין של זהב בשבת לא רצו לומר להם מותרין אתם אלא שלחום ביד עבדיהם
It also happened with Yehudah and Hillel, sons of Rabban Gamaliel, that they went out with golden slippers on Shabbat in Biri. They said to them, “We are not accustomed to go out in golden slippers on the Sabbath.” They did not want to say to them, “You are permitted.” So they sent them along with their servants.
These two follow 2.14, in which Rabbi Akiva teaches a permissive action, that Rabban Gamaliel follows in 2.15: when someone says they are not accustomed that way and he does not protest (when though he could have shared the halakhically-permitting view). Following that, we have two instances of his sons in different towns doing something rabbinically permissible, but the townsfolk are not accustomed that way. Even though they could have shared a prevailing rabbinic opinion permitting them to do so, they abide by the local customs.
What seems to emerge from these four halakhic travelogues of these two sons of Rabban Gamaliel is that they all involve their up-to-date halakhic knowledge, perhaps even moreso than the local townsfolk they encounter. (Why they are travelling to these places, however, is unclear.)