1) THE SEVERITY OF A FALSE "SHEVU'AH"
QUESTION: The Mishnah (34b) teaches that the Rabanan do not require an Almanah (widow) who wants to collect her Kesuvah to make a Shevu'ah that she did not yet collect it, but they require her to make a Neder instead. The Gemara explains that the Rabanan did not require her to make a Shevu'ah out of fear that she would swear falsely, rationalizing that she is entitled to take more money from her husband's estate, and thereby subject herself to the wrath of Hash-m for swearing falsely. Since a false Neder is not as severe as a false Shevu'ah, the Rabanan let her make a Neder instead.
The Gemara explains that according to Shmuel, the Rabanan permit an Almanah to make a Shevu'ah when she does so outside of Beis Din. RASHI (DH Chutz la'Beis Din) explains that a Shevu'ah outside of Beis Din is less severe since it is not made with the Name of Hash-m but rather with an expression of "Arur" (a malediction; the Gemara in Shevuos (39a) states that when one uses the word "Arur" in support of a promise, it is considered a Shevu'ah), and, furthermore, it is not made while one holds an object of Kedushah (such as a Sefer Torah or Tefilin).
The Gemara earlier demonstrates the severity of a false Shevu'ah through an incident in which a woman swore that she did not benefit from a Dinar that she was watching for someone else. She swore by saying, "May one of my children die from poison if I derived any benefit from that coin!" She was unaware that she had derived minimal benefit from the coin, and because her Shevu'ah was false her son indeed died.
According to Shmuel, a Shevu'ah made outside of Beis Din is not so severe since it is only an Arur and she does not hold a holy object. Why, then, was the woman who swore about the Dinar punished so severely? Her Shevu'ah was simply an Arur and was not made while she held a holy object! (RASHASH, MAHARAM SHIF)
(a) The RAMBAN and the CHIDUSHI HA'RAN on the Mishnah (34b) explain that the severity of the punishment of a false Shevu'ah is that not only is the person who made the Shevu'ah punished, but the rest of the world is punished as well, as the Gemara states in Shevuos (39a). When a Shevu'ah is made outside of Beis Din, only the person who swore falsely is punished. That is why the woman lost her son even though she swore falsely outside of Beis Din.
According to this explanation, when the Gemara cites the story of the woman with the Dinar, it is not attempting to prove the severity of a false Shevu'ah. Rather, it is showing that even when a person swears falsely by mistake, he is still subject to punishment.
However, as the Ramban points out, the Yerushalmi states explicitly that the severity of a false Shevu'ah is that it causes a person's children to die, as the story of the woman with the Dinar demonstrates (see also Shabbos 32b). Rashi (DH k'Mi she'Nishba) also seems to understand that the Gemara records this story in order to demonstrate the severity of making a false Shevu'ah.
(b) The TOSFOS RID and ME'IRI explain that the woman indeed uttered the Name of Hash-m in her Shevu'ah, and not just the words quoted by the Gemara. Even if one does not say the Name of Hash-m, perhaps a statement of Arur in which one specifies that a child should die is as severe as a Shevu'ah made with the Name of Hash-m. The Arur which Shmuel permits one to make outside of Beis Din is a simple Arur which does not include an expression of a severe punishment. Such an Arur is less severe than a Shevu'ah with the Name of Hash-m (see DIBROS MOSHE).