"Va'ye'etar Yitzchak laHashem l'nochach ishto..." Rashi paints a picture for us: Yitzchak was in one corner of the room, Rivka in the opposite corner, each one davening for a child. The description is vivid, but what bothers me is why it is necessary at all. Who cares if Yitzchak and Rivka were standing in opposite corners, in the same corner, in different rooms, in the same room? Since when is the chumash concerned with painting a scene for us? What matters is that they davened, period, full stop -- not where they stood in relation to each other. I'm not sure what according to Rashi the point here is (assuming you understand Rashi literally -- see Maor vaShemesh for a kabbalistic derash).
I actually started thinking about this phrase "l'nochach ishto" two weeks ago when we read the haftarah of VaYeira. The navi there describes how Elisha put his mouth on the mouth of the dead son of the Isha Shumanis, placed his eyes against his eyes, his hands on his hands, etc. It sounds like he is doing CPR, but the child was brought back to life miraculously, not by medical intervention (according to most views). So why did Elisha need to go through this whole act? Radak answers that Elisha was doing it to arouse his kavanah. He need the child in his proximity, he needed the physical closeness to atune himself to the situation and focus on it. Continues Radak, this is just like Yitzchak daveing "l'nochach ishto." Yitzchak needed Rivka's presence there to focus himself on her plight. (Parenthetically, for those who pace during davening, I think you have a makor in that haftarah -- "vayashav va'yeilech babayis achas heina v'achas heina.." See Radak there as well.) Maybe this is why we place our hands on our children when we bless there before Shabbos or before Y"K. The physical closeness is there to bring our kavanah to its maximum.
The simplest pshat in "l'nochach ishto" is, I think, the Rashbam, who writes that it means simply "bishvil ishto," for Rivka's sake. But this begs the question: doesn't that go without saying? For whose sake other than Rivka's could he have been praying? "Ishto" as opposed to who? Seforno anticipates the question and writes that Yitzchak prayed that his children he would come from Rivka, the most suitable wife for him. In other words, he wanted to avoid having to take another wife to have children.
Maybe there is more to it, however, than that. The Taz in Divrei David raises two (actually more - take a look) fundamental questions on the parsha. 1) Before telling us about Yitzchak's tefilah, the parsha reminds us that Rivka was "bas Besuel ha'Arami... achos Lavan." Rashi comments that the Torah comes to praise Rivka. She grew up in a home of idolaters, and nonetheless was a tzadekes. Yet, just one pasuk later the Torah tells us, with respect to Yitzchak's tefilah, "va'yei'aser LO Hashem," Hashem listened to HIS tefilah. It was to Yitzchak that Hashem responded, not Rivka (according to Rashi, who assumes both were praying independently). It seems incongruous. On the one hand, the parsha opens with lavish praise of Rivka, only to set us up for her prayer being rejected due to a shortcoming in her background, at least in comparison to Yitzchak. 2) We already know who Rivka is from last week's parsha. We know she grew up in the home of Lavan and Besuel and rose above their bad influence. Why inject a retelling of her background here?
The Yismach Moshe suggests a radical pshat in "l'nochach ishto" that will resolve both problems. Yitzchak viewed himself as continuing the legacy of his father -- there was nothing original or groundbreaking in what he was doing. Rivka, on the other hand, had forged her own path to avodah. The opening of the parsha recounts Rivka's background perhaps to set up the tension between these two approaches. On the one hand, "Yitzchak ben Avraham" and "Avraham holid es Yiztchak," the parsha emphasizes Yitzchak's connection with his father, with the past, with a path that was already forged, vs. "Rivka bas Besuel... achos Lavan," coming from nothing and forging a new path.
Yitzchak believed, says the Yismach Moshe, that Rivka had the edge on him. He davened, "l'nochach ishto," invoking her merit as the basis by which G-d should grant them children. Originality trumps mere fidelity to the past. "Ishto" here is not to the exclusion of some other potential wife, but rather to the exclusion of Yitzchak himself, to the exclusion of his own merits, which he thought insufficient.
How does G-d respond? "Va'yei'aser LO," G-d responded to Yitzchak's own prayer. Three possible ways to read this: 1) According to Rashi, G-d responded to Yitzchak, not Rivka. The zechus of the tzadik ben tzadik in facts trumps the merit of the tzadik ben rasha. Following in the footsteps of the past trumps those who must make their own way. 2) Given the Yismach Moshe's understand of the first half of the pasuk, perhaps the meaning here is that G-d responded to Yitzchak davka because he invoked his wife's merits. 3) Finally, and most radically, the Yismach Moshe's own reading is that G-d responded "lo," to Yitzchak as an individual, as opposed to Yitzchak the extension of his father Avraham. G-d's message to Yitzchak was that his avodah was not merely a replay of his father's life, and therefore devoid of originality, but rather he too stood on his own merits, had his own path, he too had his own way to carve just as Rivka had carved her own (albeit in a more extreme set of circumstances.)
To take one more step, perhaps the tension here between the zechus of following in the foosteps of the past vs. carving a new path is davka highlighted in the context of Yitzchak and Rivka's tefilah for children because the Torah is asking us to consider what we expect from our children -- do we want them to merely walk in our foosteps, or are we davening for a new generation that will carve their own path and move off in a new direction of their own? And perhaps the better question is not which approach we expect from our children, but which approach we aspire to ourselves.