The Shulchan Aruch (141:6) rules that although it is permissible according to the strict Halacha to call two brothers or a father and son for successive Aliyot to the Torah, this is not done due to the concern of Ayin Ha'ra (the evil eye). Chacham David Yosef (son of Chacham Ovadia Yosef), in his work Halacha Berura (vol. 7, p. 212), adds that this applies as well to a grandfather and grandson; they should not be called for successive Aliyot due to the risk of Ayin Ha'ra. A Halachic principle establishes that "Benei Banim Harei Heim Ke'banim" one's relationship to his grandchildren is the same for purposes of Halacha as one's relationship to his children. Thus, just as a father and son should not be called to the Torah for successive Aliyot, so should successive Aliyot not be given to a man and his grandson.
Some authorities, however, as Chacham David notes, are lenient in this regard, and allow calling a grandfather and grandson for successive Aliyot. He writes that where it is necessary, such as when a family is celebrating an occasion and many family members are receiving Aliyot, they may rely on the lenient position. Our practice, however, follows the stringent view, which forbids calling a grandfather and grandson for successive Aliyot. This is particularly so in cases of a grandfather and grandson who share the same name; in such a case, according to all opinions they may not be called to the Torah for successive Aliyot.
On the following page (p. 213), Chacham David writes that two brothers, a father and son, and a grandfather and grandson may be called for successive Aliyot that are read from two different Torah scrolls. On Yom Tov, for example, a second Torah scroll is opened for the Maftir reading, and it would thus be permissible to call two relatives for the final Aliya read in the first Torah and Maftir. Even though these are two successive Aliyot, nevertheless, the opening of a new Torah scroll for the Maftir reading constitutes a significant enough interruption to allow calling for Maftir a relative of the person called for the previous Aliya. This applies as well in situations where a second Torah is used for the Maftir reading on Shabbat, such as on Shabbat Zachor or Shabbat Rosh Chodesh.
Another example of this situation is Simchat Torah, when we open a second Torah for the reading of Chatan Bereishit. A synagogue may call for Chatan Torah and Chatan Bereishit a father and son, two brothers, or a grandfather and grandson, despite the fact that these are successive Aliyot. Once again, the opening of a second Torah marks an interruption that allows calling a relative for the subsequent Aliya. Likewise, on Chol Ha'mo'ed Pesach, the first three Aliyot are read from one Torah, and the fourth from a second Torah. It would thus be permissible to call two relatives for the third and fourth Aliyot, since these Aliyot are read from separate Torah scrolls.
Finally, Chacham David rules that a father-in-law and son-in-law may be called for successive Aliyot in situations where this is necessary, such as if a family is celebrating an occasion in the synagogue and many family members are called for Aliyot.
The same Halacha we learn here applies to two Kohanim as well, who can be regarding similar to the relationship of grandfather, son, grandson. For more details, see the Halacha entitled Simhat Torah- Is It Permissible For 2 Kohanim or 2 Leviim To Have A Back To Back Aliyah at the Torah.
Summary: A congregation should not call for successive Aliyot to the Torah a father and son, two brothers, or a grandfather and grandson, except for successive Aliyot that are read from two different Torah scrolls. A father-in-law and son-in-law may be called for successive Aliyot even from the same Torah scroll in situations where this is necessary.
