I am not sure I understand the question-- in Jewish law, it is the get that produces a divorce. If your divorced parents do not yet have a get, they are still married according to Jewish law. Illegitimacy as you refer to it would happen if a woman who was not yet properly divorced-- meaning, by Jewish law, she was still married-- entered into what she thought of as another marriage. While her intentions are innocent, if she is not legally divorced (or, in this case, halachically), it is the same as if she is having an affair, and any children from that "affair" carry the stigma of being the product of a prohibited sexual relationship. It is, halachically, the same as if she became pregnant from an affair, which is, in turn, the same as if she became pregnant (regardless of marriage) from having incestuous relations, like with a son or nephew.
Once such children are born, the question becomes whether there is a way to retroactively improve that status. Sometimes, the validity of the original marriage is called into question, which would mean the woman was never married, and then the second marriage is not an adulterous one. Rabbis strive mightily to help the children avoid this stigma, because it places several halachic burdens on those children, but it must be done individually, judging each case by its specifics.
In your question, if you meant that your parents had previously been divorced, and then married each other, producing you, the question would be whether the first marriage (on your mother's side) was ended properly. If it was not, and she simply receives a get now, that would not affect your halachic status. There are occasions, however, when rabbis can construct remedies to this problem even after the fact, but they are too individual and tailored to share in a forum like this.
QUESTION: If my divorced parents get a GET, does that make me and my siblings illegitimate?
The short answer: absolutely not!
The GET – the traditional instrument of Jewish religious divorce – dissolves a valid marriage between Jewish partners. While the breakdown of a marriage is a sad occurrence, a GET in no way affects the religious status or “legitimacy” of children born during the course of that marriage.
Illegitimacy in Jewish Law – mamzerut – occurs only when a child is born of an incestuous union, or to a woman who – at the time of conception – was bound by a valid Jewish marriage to a man other than the child’s father. A child born to an unmarried mother (and whose father would have been permitted to her in marriage) is not a mamzer – no taint of illegitimacy devolves on such a child. This distinguishes Jewish views of “legitimacy” and “illegitimacy” from the popular Western notion. Thus even if you and your siblings had been born to your parents without benefit of marriage whatsoever, you would have no stigma of “illegitimacy” in Jewish Law.
By securing a GET (a process over which I officiate regularly as a Mesader Gittin, an authorized adjudicator of Jewish religious divorce), your parents actually honor the sanctity of their marriage by dissolving that union in keeping with the strictures of Jewish Law and tradition. That is, they observe a Mitzvah, a divine commandment.
Far from leading to illegitimacy, the issuing of a GET actually prevents mamzerut, as it removes the possibility that subsequent, intimate relationships of either of the divorcing parties could be deemed adulterous. Children born to a woman in a second marriage (or outside of marriage) without benefit of a GET to dissolve her first marital union (and regardless of any civil divorce proceeding) are, indeed, mamzerim.
Furthermore, even if a Jewish marriage is annulled retroactively by Rabbinic authorities (through Hafka’at Kiddushin – a process rarely invoked today, but still administered by the Joint Bet Din of the Conservative Movement, of which I am a member), children born during the course of the putative marriage would still be “legitimate.” In fact, the taint of mamzerut is removed from children born of an adulterous union if the original marriage which rendered their parents’ union adulterous itself is annulled by rabbinic authorities based on just cause. The “legitimation” of mamzerim, however, is not acceptable grounds for annulment proceedings in Jewish law – only an occasional, fortunate (if unintended) consequence.
The Talmud states that the stones of the very altar in the Holy Temple weep when a formerly loving marriage is dissolved through divorce. My teacher, Rabbi Edward Gershfield, a master Mesader Gittin, put it still more succinctly: “In Judaism, divorce is not a sin; it is a tragedy.” I wish your parents renewed happiness and success. You and your siblings – blessings born of your parents’ “holy matrimony” – can admire them further for concluding their marriage with concern for its sacred status. Notwithstanding the conflict and sadness typically associated with divorce, that is “legitimate” grounds for gratitude.
In a word, no. A get does not mean that the a marriage never took place. Even if one is born out of wedlock, a Jewish child is not viewed as illegitimate. That is a British common law term. The term "Momzer" does not mean an illegitimate child, as popular ignorance would have us believe. It is a halachic term referring to a child born to an incestuous or other forbidden relationship, such as a Kohen and divorced woman.
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