The translation "rival" for לצרור is an over-literal and uncertain translation, but perhaps the best we can do in English.
The MT of Leviticus 18:18 is:
וְאִשָּׁ֥ה אֶל־אֲחֹתָ֖הּ לֹ֣א תִקָּ֑ח לִצְרֹ֗ר לְגַלּ֧וֹת עֶרְוָתָ֛הּ עָלֶ֖יהָ בְּחַיֶּֽיהָ
The only other verse that we have for direct comparison is I Samuel 1:6 (NIV)
Because the LORD had closed Hannah's womb, her rival kept provoking her in order to irritate her
For which the MT is:
וְכִעֲסַ֤תָּה צָרָתָהּ֙ גַּם־כַּ֔עַס בַּעֲב֖וּר הַרְּעִמָ֑הּ כִּֽי־סָגַ֥ר יְהֹוָ֖ה בְּעַ֥ד רַחְמָֽהּ
Most of the early commentators see לצרר in Leviticus 18:18 and צרתה in I Samuel 1:6 as coming from the word צר, meaning a rival or tormentor. However, there is a possibility that צר is from the same root at צרור, meaning to string together, like beads on a necklace or like coins confined in a purse as in Genesis 42:35 (NIV):
As they were emptying their sacks, there in each man's sack was his pouch of silver! When they and their father saw the money pouches, they were frightened
For which the MT is:
וַיְהִ֗י הֵ֚ם מְרִיקִ֣ים שַׂקֵּיהֶ֔ם וְהִנֵּה־אִ֥ישׁ צְרוֹר־כַּסְפּ֖וֹ בְּשַׂקּ֑וֹ וַיִּרְא֞וּ אֶת־צְרֹר֧וֹת כַּסְפֵּיהֶ֛ם הֵ֥מָּה וַאֲבִיהֶ֖ם וַיִּירָֽאוּ
So a man with multiple wives as a "string" of wives. Support for this translation comes from II Samuel 20:3 (NIV):
When David returned to his palace in Jerusalem, he took the ten concubines he had left to take care of the palace and put them in a house under guard. He provided for them but had no sexual relations with them. They were kept in confinement till the day of their death, living as widows
For which the MT is:
וַיָּבֹ֨א דָוִ֣ד אֶל־בֵּיתוֹ֮ יְרוּשָׁלִַ֒ם֒ וַיִּקַּ֣ח הַמֶּ֡לֶךְ אֵ֣ת עֶשֶׂר־נָשִׁ֣ים ׀ פִּלַגְשִׁ֡ים אֲשֶׁ֣ר הִנִּ֩יחַ֩ לִשְׁמֹ֨ר הַבַּ֜יִת וַֽיִּתְּנֵ֤ם בֵּית־מִשְׁמֶ֙רֶת֙ וַֽיְכַלְכְּלֵ֔ם וַאֲלֵיהֶ֖ם לֹא־בָ֑א וַתִּהְיֶ֧ינָה צְרֻר֛וֹת עַד־י֥וֹם מֻתָ֖ן אַלְמְנ֥וּת חַיּֽוּת
In this verse, the NIV and most other translations translate צרורות (tsrurot) as "in confinement", though IMHO this is a reference to their being in a perpetually married state as צרות, multiple wifes of one man, which does in fact confine them, i.e. prevent them from marrying other men, but in a legal sense, not in a physical sense, as the verse has already stated that in the physical sense of confinement they had been "put [them] in a house under guard".
There is no other term than צרה (tsarah) in any historical period of the Hebrew language to indicate the relationship between two or more women who have the same husband. So צרה is a term of familial relationship that is essential to the spoken language no less than "uncle", "nephew", "mother-in-law" or any other common term of familiar relationship. Since there is no corresponding term for this familiar relationship in English that the translators could use, it appears that they have defaulted to "rival" on the assumption that the the root is צר in the sense of tormentor or rival.
In later Hebrew the use of the term צרה for a second or third wife, the connotation of rivalry is not important, which hints that meaning in the OT is not necessarily a "rival" wife but simply an "other" or "additional" wife.
The term is still used on modern Hebrew to denote one or the other or both wives of a man with more than one wife, with no connotation of rivalry. It is also used figuratively to indicate the relationship of two or more of some type of thing that is denoted by a noun of feminine noun class, that have the same type of relationship to a specific thing that is denoted by a noun of masculine noun class.