Many sources[1] indicate that there is a mitzva from the Torah to read Parashat Zachor, which is made up of a number of p’sukim found at the end of Ki Teitzei.[2] This assertion finds support in the gemara,[3] which derives that Megillat Esther must be read from a proper scroll based on a scriptural comparison to the mitzva to remember the actions of Amalek, which HaShem commanded Moshe to write down in a “book.”[4] The gemara continues that although one can fulfill the mitzva “not to forget” what Amalek did by reading silently, we must read about their actions aloud because the Torah also says to “remember,” which indicates doing a positive action. The Terumat HaDeshen[5] infers from the Rosh[6] that the Torah requirement includes the need for a minyan. Therefore, the Shulchan Aruch[7] stipulates that because Parashat Zachor is a Torah mitzva, one should go to a place with a minyan for Shabbat Zachor to hear the Torah reading – hence, your predicament.
Let us see if there are any mitigating circumstances that can lessen the obligation or provide alternatives. Not all the Rishonim who mention the Torah-level obligation to read Parashat Zachor indicate that the obligation can be met only at the time and in the manner that we normally carry it out. The Sefer HaChinuch,[8] for one, says that the Torah law may possibly be fulfilled by a reading every couple of years, before one forgets the story. Others[9] explain that Chazal felt it necessary to institute the reading once a year because one tends to forget things after twelve months.[10] (See the discussions in Shut Chatam Sofer[11] and the Maharam Shick[12] about the problem that in a leap year there are thirteen months between the special readings of Zachor.)
The Magen Avraham[13] notes that in his time, people were not very careful to hear Parashat Zachor. He justifies the practice by suggesting that they heard the story of Amalek in the kri’at haTorah of Purim morning.[14] Many take issue with this suggestion because the Purim reading does not connect the story to the mitzva to wipe out the remembrance of Amalek.[15] If this were the only difficulty, one could solve it by hearing the p’sukim of Zachor when Parashat Ki Teitzei is read. However, this solution also entails complications. First, one probably has to have in mind to fulfill the specific mitzva to remember Amalek through that reading, and he likely even has to alert the ba’al koreh to have this intention in mind for all those listeners who want to be included.[16] (The Taz[17] says that the berachot are also an absolute requirement, so in his view, the oleh might also need to have him in mind.) Furthermore, if you plan to do use this tactic in the coming year but did not do so last year, 18 months will have gone by in between readings, which, as we saw above, is problematic.
The Rama[18] says that if one is unable to attend a public reading of Parashat Zachor, he should read it by himself. Ideally, this should be done from a sefer Torah,[19] which is probably not available to you. However, on that Shabbat, one should at least accomplish the mitzva “not to forget” Amalek’s actions through any clear review of the subject matter. Although Chazal established a specific time and manner in which to fulfill the positive mitzva, it is likely that one can fulfill the Torah obligation by individually reading the p’sukim from a sefer Torah before or after your trip.[20]
Despite the mitigating factors and alternatives, the Shulchan Aruch’s simple ruling still seems to require you to make every reasonable effort to be in a place where you can hear the public reading of Parashat Zachor at its time. There are circumstances, however, in which a person cannot arrange to fulfill a mitzva. It is difficult to provide exact guidelines, but we can address your specific situation if you wish to share it with us.