B"H
First, that reference from Deuteronomy 22:13-15 (really extending to -20 and on) is talking about a case where she cheated on him after becoming engaged to him but before marrying him, which is a capital offense.
Rashi ibid:20
- But if this matter was true: [indeed,] no evidence of the girl's virginity was found. כ. וְאִם־אֱמֶ֣ת הָיָ֔ה הַדָּבָ֖ר הַזֶּ֑ה
לֹֽא־נִמְצְא֥וּ בְתוּלִ֖ים לַנַּֽעֲרָֽה (כתיב לנער)
But if this
matter was true: [as corroborated] by witnesses, and there was
warning, [proving] that she had committed adultery after her
betrothal. — [Keth. 44b]
וְאִם־אֱמֶת הָיָה הַדָּבָר: בְּעֵדִים וְהַתְרָאָה, שֶׁזִּנְּתָה
לְאַחַר אֵרוּסִין (כתובות מ"ד):
According to Torah law, a man is allowed to have more than one wife, but not the other way around. There's no unique "sin" for a man to commit adultery as there is for a woman (besides for the other sins involved for having relations with someone he's not married to/a niddah etc), although if he does cheat on her then that is grounds for her to initiate a divorce (see later).
In terms of being "fair" and "moral": morality is defined by the Creator. He made everything, He decides what's good and what's bad.
The Rambam tells us that all of the laws of forbidden relationships are known as chukim, Mitzvos who's reasoning is not known to us.
They have deep spiritual reasons, some that only the Creator knows about, but not all of them can be understood by the intellect of created beings.
The Rambam does say that however much reason one can give these commandments, one should give (end of h. Meila), but (ibid) the main reason of them is still hidden from us.
In terms of a woman being able to divorce a man because of immodest behavior, many rabbis say that if she simply doesn't want to continue being with him then she can initiate a divorce, especially if the man has been involved excessively with other women, even when no adultery was found.
A woman may demand a divorce from her husband, if he has been found to
be philandering with other women. There need not be proof of his
having committed adultery, just of his having cavorted with other
women. Even his causing her a bad name through his lecherous actions
is likewise considered legitimate justification for the wife launching
a divorce action. If the wife feels repulsed by her husband, it is
wrong to force her to remain in the union
Now to the question of what specifically is meant by "immodest behavior" by the women, the Rambam references the verse in hilchos geirushin 10:20-22:
22 It is a mitzvah to divorce a woman who possesses unsavory character
traits and does not conduct herself modestly73, as is the practice of
proper daughters of Israel, as [implied by Proverbs 22:10]: "Drive
away the scoffer, and contention will depart."
When a woman has been divorced for loose moral conduct,74 it is not
fitting for a proper man to marry her, lest people say: "This one sent
away this wicked woman, and this one brought her home."
כב אִשָּׁה רָעָה בְּדֵעוֹתֶיהָ וְשֶׁאֵינָהּ צְנוּעָה כִּבְנוֹת
יִשְׂרָאֵל הַכְּשֵׁרוֹת מִצְוָה לְגָרְשָׁהּ שֶׁנֶּאֱמַר (משלי כב י)
״גָּרֵשׁ לֵץ וְיֵצֵא מָדוֹן״. וְאִשָּׁה שֶׁנִּתְגָּרְשָׁה מִשּׁוּם
פְּרִיצוּת אֵין רָאוּי לְאָדָם כָּשֵׁר שֶׁיִּשָּׂאֶנָּה. שֶׁלֹּא
יֹאמְרוּ זֶה הוֹצִיא רְשָׁעָה מִבֵּיתוֹ וְזֶה מַכְנִיסָהּ:
And in hilchos ishus 24:11-12 the Rambam explains exactly what is meant:
11 The following are the actions for which a woman is considered to
have "violated the faith of Moses":
a) going out to the marketplace with her hair uncovered;25
b) taking vows or oaths that she does not keep;
c) engaging in sexual relations [with her husband] while in the niddah
state;
d) failing to separate challah or feeding her husband food that is
forbidden to eat - needless to say, this applies to forbidden crawling
animals and animals that were not ritually slaughtered; it applies
even to produce that was not tithed.26
How can the latter [two] matters be known? For example, she said: "So
and so, the priest, [separated tithes] from this produce for me," "So
and so separated challah [from this dough]," "So and so, the Sage,
said this stain does not render me a niddah" - and after eating the
food or engaging in sexual relations with her, the husband asked the
person whose name was mentioned and he denied the occurrence of the
incident. Another example: a woman's [conduct caused] it to be
established in her neighborhood that she was in the niddah state,27
but she told her husband that she was ritually pure. He engaged in
relations with her [and afterwards discovered the truth].
יא וְאֵלּוּ הֵן הַדְּבָרִים שֶׁאִם עָשְׂתָה אַחַת מֵהֶן עָבְרָה עַל
דַּת משֶׁה. יוֹצְאָה בַּשּׁוּק וּשְׂעַר רֹאשָׁהּ גָּלוּי. אוֹ
שֶׁנּוֹדֶרֶת אוֹ שֶׁנִּשְׁבַּעַת וְאֵינָהּ מְקַיֶּמֶת. אוֹ
שֶׁשִּׁמְּשָׁה מִטָּתָהּ וְהִיא נִדָּה. אוֹ שֶׁאֵינָהּ קוֹצָה לָהּ
חַלָּה. אוֹ שֶׁהֶאֱכִילָה אֶת בַּעְלָהּ דְּבָרִים אֲסוּרִים, אֵין
צָרִיךְ לוֹמַר שְׁקָצִים וּרְמָשִׂים וּנְבֵלוֹת, אֶלָּא דְּבָרִים
שֶׁאֵינָן מְעֻשָּׂרִין. וְהֵיאַךְ יוֹדֵעַ דָּבָר זֶה כְּגוֹן
שֶׁאָמְרָה לוֹ פֵּרוֹת אֵלּוּ פְּלוֹנִי כֹּהֵן תִּקְּנָם לִי וְעִסָּה
זוֹ פְּלוֹנִית הִפְרִישָׁה לִי חַלָּתָהּ וּפְלוֹנִי הֶחָכָם טִהֵר לִי
אֶת הַכֶּתֶם וְאַחַר שֶׁאָכַל אוֹ בָּא עָלֶיהָ שָׁאַל אוֹתוֹ פְּלוֹנִי
וְאָמַר לֹא הָיוּ דְּבָרִים מֵעוֹלָם. וְכֵן אִם הֻחְזְקָה נִדָּה
בִּשְׁכֵנוֹתֶיהָ וְאָמְרָה לְבַעְלָהּ טְהוֹרָה אֲנִי וּבָא עָלֶיהָ:
12 What is meant by "the Jewish faith"? The customs of modesty that
Jewish women practice. When a woman performs any of the following
acts, she is considered to have violated the Jewish faith:
a) she goes to the marketplace or a lane with openings at both ends
without having her head [fully] covered - i.e., her hair is covered by
a handkerchief, but not with a veil like all other women,28
b) she spins [flax or wool] with a rose on her face29 - on her
forehead or on her cheek - like immodest gentile women,
c) she spins in the marketplace and shows her forearms to men;30
d) she plays frivolously with young lads,
e) she demands sexual intimacy from her husband in a loud voice until
her neighbors hear her talking about their intimate affairs, or
f) she curses her husband's father in her husband's presence.31
יב וְאֵי זוֹ הִיא דָּת יְהוּדִית הוּא מִנְהַג הַצְּנִיעוּת שֶׁנָּהֲגוּ
בְּנוֹת יִשְׂרָאֵל. וְאֵלּוּ הֵן הַדְּבָרִים שֶׁאִם עָשְׂתָה אַחַת
מֵהֶן עָבְרָה עַל דָּת יְהוּדִית. יוֹצְאָה לַשּׁוּק אוֹ לְמָבוֹי
מְפֻלָּשׁ וְרֹאשָׁהּ פָּרוּעַ וְאֵין עָלֶיהָ רְדִיד כְּכָל הַנָּשִׁים.
אַף עַל פִּי שֶׁשְּׂעָרָהּ מְכֻסֶּה בְּמִטְפַּחַת. אוֹ שֶׁהָיְתָה
טוֹוָה בַּשּׁוּק וּוֶרֶד וְכַיּוֹצֵא בּוֹ כְּנֶגֶד פָּנֶיהָ עַל
פַּדַּחְתָּהּ אוֹ עַל לְחָיֶיהָ כְּדֶרֶךְ שֶׁעוֹשׂוֹת הָעַכּוּ''ם
הַפְּרוּצוֹת. אוֹ שֶׁטּוֹוָה בַּשּׁוּק וּמַרְאֵית זְרוֹעוֹתֶיהָ
לִבְנֵי אָדָם. אוֹ שֶׁהָיְתָה מְשַׂחֶקֶת עִם הַבַּחוּרִים. אוֹ
שֶׁהָיְתָה תּוֹבַעַת הַתַּשְׁמִישׁ בְּקוֹל רָם מִבַּעְלָהּ עַד
שֶׁשְּׁכֵנוֹתֶיהָ שׁוֹמְעוֹת אוֹתָהּ מְדַבֶּרֶת עַל עִסְקֵי
תַּשְׁמִישׁ. אוֹ שֶׁהָיְתָה מְקַלֶּלֶת אֲבִי בַּעְלָהּ בִּפְנֵי
בַּעְלָהּ: