Why does ואת עמלני refers to sons specifically?

Summary: Rav Chaim Kanievsky explains, based on a gemara that רוצה לעשות כל בניו זכרים יבעול וישנה, which entails greater tircha. And this is related to the beginning of parashat Tazria, and the famous derasha about how to have male children.

Post:
The famous derasha in the Haggada is that  ואת עמלני refers to the sons, whom Pharaoh ordered cast in the Nile. But it is non-obvious why that should refer specifically to the banim.

I saw the following in Taama deKra, by Rav Chaim Kanievsky:

ואת עמלנו אלו הבנים כמו שנא׳ כל הבן
 הילוד וגו. וקשה למה הבנים נקראין עמלנו טפי
 מהבנות, וי״ל משום דאמרי׳  בעירובין ק׳ ב׳
 הרוצה לעשות בניו זכרים יבעול וישנה ואמרי׳
 שם שאסור לבעול ולשנות בלא דעת האשה
 והיינו שמטריחה  ביותר כדפירש״י לכן קרי  לה
 ואת עמלינו.

"That is, why are sons called 'our toil' more so than daughters? There is to say, based on Eruvin daf 100b, that one who wishes to have male children should have intercourse and then repeat. And we say there that it is forbidden to have intercourse and then repeat without the consent of the wife. And this is because it troubles her excessively, as Rashi explains. Therefore it is rightly called  ואת עמלינו."

The gemara in Eruvin reads:

ואמר רמי בר חמא אמר רב אסי אסור לאדם שיכוף אשתו לדבר מצוה שנאמר ואץ ברגלים חוטא וא"ר יהושע בן לוי כל הכופה אשתו לדבר מצוה הווין לו בנים שאינן מהוגנין אמר רב איקא בר חיננא מאי קראה (משלי יט, ב) גם בלא דעת נפש לא טוב תניא נמי הכי גם בלא דעת נפש לא טוב זה הכופה אשתו לדבר מצוה ואץ ברגלים חוטא זה הבועל ושונה איני והאמר רבא הרוצה לעשות כל בניו זכרים יבעול וישנה ל"ק כאן לדעת כאן שלא לדעת:

Or, in English (citing my translation of the Rif):

And Mari bar Abba cited Rav Ashi {our gemara: Rami bar Chama cited Rav Assi}: It is forbidden to compel {=force} one's wife to engage in a mitzvah {=marital relations}, for it is stated {Mishlei 19:2}:

ב גַּם בְּלֹא-דַעַת נֶפֶשׁ לֹא-טוֹב ;וְאָץ בְּרַגְלַיִם חוֹטֵא.

2 Also, that the soul be without knowledge is not good; and he that hasteth with his feet sinneth.

{and raglayim is a common Biblical allusion to genitals.}

Rabbi Yehoshua ben Levi said: Whoever compels his wife to engage in a mitzvah {=marital relations} will have unworthy children.

Rav Ika bar Chanina said: What is the Scriptural reference? {The first part of the same pasuk:}

ב גַּם בְּלֹא-דַעַת נֶפֶשׁ לֹא-טוֹב; וְאָץ בְּרַגְלַיִם חוֹטֵא.

2 Also, that the soul be without knowledge is not good; and he that hasteth with his feet sinneth.

{perhaps: also without daat = consent; there will be a soul, person = nefesh born who is not good}

A brayta also says so: גַּם בְּלֹא-דַעַת נֶפֶשׁ לֹא-טוֹב - this is one who compels his wife to engage in a mitzvah {=marital relations}. וְאָץ בְּרַגְלַיִם חוֹטֵא - this is one who has intercourse and then repeats.

Is this so? But Rava said: One who wants male children should have intercourse and repeat! This is no question. Here {=the former,where it is a sin} is without her consent, and here {the latter, where it is no sin} is with her consent.

And Rashi on that gemara reads:

הבועל ושונה - שמטריחה:

לדעת - האשה:

יבעול וישנה - שמחמת ביאה ראשונה נתאוה האשה והולבשה תאוה וכשבא ביאה שניה היא מזרעת תחילה והיכא דהיא מזרעת תחילה יולדת זכר:

I am not certain that I agree with Rav Kanievsky's rendition of the gemara in Eruvin. After all, it is not just הבועל ושונה which must be with consent, but indeed every sort of intercourse. And שמטריחה does not mean that she is bothered, in the sense of finding it annoying, troublesome, and hard work, but rather that he has intercourse and continues at it with her. And indeed, looking at the Rashi in d"h יבעול וישנה, it is clear that this first ביאה awakens תאווה such that as he continues, she will be מזרעת first.

This seems far from the characterization in Taama deKra.

Even so, this is something that requires more effort on the part of both participants, such that it could well be considered  ואת עמלני. And Rashi's explanation, that this will cause the woman to give seed first is quite plausible in explaining this gemara. After all, this is accordance with the theory, described in Niddah 31a, that if the woman gives forth seed first, then she will give birth to males. And this, in turn, is based on the beginning of this week's parasha, Tazria:

א וַיְדַבֵּר ה אֶל-משֶׁה לֵּאמֹר: 
ב דַּבֵּר אֶל-בְּנֵי יִשְׂרָאֵל לֵאמֹר אִשָּׁה כִּי תַזְרִיעַ וְיָלְדָה זָכָר וְטָמְאָה שִׁבְעַת יָמִים כִּימֵי נִדַּת דְּוֹתָהּ תִּטְמָא: 

See also the Ramban on this, where he advances the gemara's theory and explains it in terms of Greek science.

So perhaps it was just an editing error in Taama deKra, and he meant to simply say that, based on הבועל ושונה defined as שמטריחה, there is greater effort, such that male children can rightly be called amaleinu, more so than daughters.

Even so, I don't think that this is "pshat" in the derasha in the Haggadah. I am not truly convinced that the Haggadist meant to highlight sons rather than daughters in ואת עמלנו. Rather, the decree happened to be on the sons, and thus involved destroying some children of the Hebrews. And just as anyeinu was one aspect of the decree, the prishut derech eretz, and lachatzeinu was another aspect of the decree (perhaps), so too amaleinu was another aspect of the decree. So we should not be looking to explain it in terms of sons vs. daughters.