The Torah forbids a Kohen from marrying a divorced woman (Vayikra 21:7). Even if a Kohen was married and divorced, he may not remarry his wife, as this would violate the prohibition against his marriage to a divorcee.
If a Kohen does marry a divorced woman, what is his status with regard to Birkat Kohanim and being called for the first Aliya to the Torah?
The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909), in his work Od Yosef Chai (Parashat Tetzaveh, 5; listen to audio for precise citation), rules that a Kohen who marries a divorcee may not participate in Birkat Kohanim or be called for the first Aliya. Even if the Kohen divorces the woman, or if the woman dies, he may not join Birkat Kohanim or be called for the first Aliya until he declares a formal Neder (vow) that he will not derive any benefit from the women whom the Torah forbids him to marry. Only by making such a vow does the Kohen express his sincere and unconditional remorse for having transgressed this violation, such that he may once again be afforded the status of Kohen with respect to Birkat Kohanim and the first Aliya to the Torah.
The Ben Ish Chai applies this ruling even to the case of a Kohen who marries a "Chalutza," a woman who underwent the process of "Chalitza." (The term "Chalitza" refers to the ceremony performed when a man dies without children, in which case the deceased's brother must either marry the widow or perform this ceremony.) Torah law allows a Kohen to marry a "Chalutza," but the Rabbis enacted a prohibition against such a marriage. The Ben Ish Chai writes that despite the lower level of prohibition that applies to a Kohen's marriage to a "Chalutza," a Kohen who transgresses this provision is considered to have married a divorcee, and he loses his status as Kohen with respect to the laws mentioned earlier.
In the subsequent passage (Parashat Tetzaveh, 6), the Ben Ish Chai comments that the children born from a Kohen's marriage to a divorcee do not have the status of Kohanim at all. As such, they may even become Tamei (ritually impure) by coming in contact with corpses and visiting cemeteries. This Halacha does not apply, however, to children born from a Kohen's marriage to a Chalutza. As mentioned, such a marriage is valid according to Torah law, and was forbidden later through Rabbinic enactment. Hence, the children are considered full-fledged Kohanim and therefore may not come in contact with corpses or visit cemeteries.
In this context, the Ben Ish Chai discusses as well some general laws of Tum'at Kohanim – the prohibition for a Kohen to come in contact with a dead body. He notes that this prohibition applies only to male Kohanim; daughters of a Kohen are permitted to visit cemeteries and come in contact with a dead body. Furthermore, a Kohen is permitted to come in contact with the remains – or attend the funeral – of his seven immediate relatives: father, mother, son, daughter, wife, brother and unmarried sister. A Kohen may not come in contact with the remains of his sister after her marriage, even if she has since been widowed or divorced, as mentioned by the Kesef Mishneh (commentary to the Rambam's Mishneh Torah by Rabbi Yosef Karo, author of the Shulchan Aruch), in Hilchot Avel (chapter 2).
Summary: It is forbidden for a Kohen to marry a divorcee or a woman who has undergone Chalitza. A Kohen who violates this law may not recite Birkat Kohanim or be called for the first Aliya – even after he divorces the woman or she dies – until he vows not to derive any benefit from women whom he may not marry. Children born from a Kohen's marriage to a divorcee are not considered Kohanim at all and may attend funerals; children born from a Kohen's marriage to a woman who had undergone Chalitza are still considered Kohanim. Daughters of Kohanim are permitted to attend funerals and come in contact with dead bodies. Kohanim are allowed to attend the funeral of their parents, children or siblings, with the exception of a sister who has married, even after she has been divorced or widowed.
