It is not clear what you mean by “separated some challa,” and the answer to your question depends on this point.
Among the mishna’s[2] long list of Rabbinic prohibitions of Shabbat and Yom Tov is taking terumot and ma’asrot,[3] which includes the separation of challa.[4] Therefore, if your sons’ hosts indeed performed hafrashat challa on Shabbat, they apparently acted improperly. There is a leniency to take ma’asrot in a case in which one does not have alternative food to eat for Shabbat, due to the mitzva of eating on Shabbat,[5] but this is permitted only during bein hashemashot.[6]
If the hosts improperly separated challa on Shabbat, your sons would still have been permitted to eat the remaining portion of the bread.[7] This is because if one took ma’asrot on Shabbat unintentionally (including out of ignorance of the halacha[8]), the food may still be eaten.[9] (Many discuss the question of why we do not say that the food is muktzeh for all of Shabbat, since it was not fit to be eaten when Shabbat began. In any event, it seems that it indeed is not muktzeh.[10])
It is possible that the hosts did not intend to actually proclaim, and thereby create, the challa on Shabbat, but rather simply left over enough of the bread to take challa from it after Shabbat was over. There are circumstances in which this is permitted, but if this is what the hosts did, they misapplied this leniency. Shmuel says: “Regarding the taking of challa of chutz la’aretz, one may eat now and take off the challa later.”[11] This is different from the situation regarding ma’asrot; until ma’aser has been taken, the produce is forbidden to eat (tevel). But Shmuel clearly states that this halacha is true only regarding chutz la’aretz, and, of course, Bnei Brak is in Eretz Yisrael.
One might argue that Shmuel’s leniency should apply even in Israel of our time. The Tur[12] explains that dough that carries a Rabbinic-level obligation to have challa taken from it has several leniencies compared to one that has a Torah-level obligation. One such leniency is that in the case of a Rabbinic-level obligation, the bread that has not had challa taken from it does not have the status of forbidden tevel. The obligation to separate challa outside Eretz Yisrael is certainly only Rabbinic.[13] There is a significant Talmudic machloket regarding whether the obligation of challa in Eretz Yisrael in our times is of a Torah or Rabbinic level.[14] The more accepted opinion is that even in Eretz Yisrael, challa is a Rabbinic obligation nowadays.[15] Accordingly, it might seem that even in Israel there are grounds to be lenient and allow one to eat the bread from which challa was not yet taken, leaving some to use for the hafrasha after Shabbat is over, as Shmuel suggests.
In truth, however, this is not the case. The Beit Yosef[16] rejects the above reading of the Tur, proving that even if challa in chutz la’aretz at all times and challa in Eretz Yisrael in our times are both Rabbinic obligations, the status of challa in Eretz Yisrael in our day is of a higher level, since it is modeled after the Torah law that fundamentally applies in Eretz Yisrael. This is in contrast to challa in chutz la’aretz, which has “no root in Torah law.” Therefore, if in your sons’ case the challa was taken only on Motzaei Shabbat, the bread that they ate on Shabbat had a Rabbinic status of tevel, which is forbidden to eat.
In summary, if the hosts took challa on Shabbat itself, they violated Shabbat Rabbinically, but the bread was still permitted to be eaten, provided they did not realize that their action was forbidden. If they left over bread from which to do hafrashat challa after Shabbat, it was forbidden Rabbinically to eat the bread before the hafrasha actually took place.