I remember reading of an opinion that allows married women not to cover their hair when they are in their own home in the presence of three men or less.
I cannot remember the source though and would really appreciate some help.
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The short answer(s):
(a) Rashi, Tosafot, the Ran, the Rosh, the Tur (according to the Rema in Darkei Moshe EH 115 #4) and the Shulchan Aruch (EH 21:2, 115:4) all understand the Mishna/Gemara on Ketubot 72a to mean that a woman has no obligation (a priori) to cover her hair in her courtyard, and certainly not at home, even though it may be praiseworthy to do so. So concludes Rav Moshe Feinstein (EH I.58, YD II.75, OC V.37) and says that this was the custom in previous generations. However, Rav Moshe specifically says this is only when no one other than her husband or children are present.
The Rosh (Ketubot ch. 7 #9) quotes the Yerushalmi about a courtyard: "A courtyard which the many pierce is like an alleyway [i.e. a public space]; a courtyard which the many do not pierce is like a courtyard [and therefore does not require hair covering]". It is possible to infer from this that similarly a house which "the many do not pierce" (sh'ain harabim bok'im bo) is a private space and doesn't require hair covering, and since in other places three people is considered "public" (for example with respect to Lashon Hara/Gossip), a woman need not cover her hair at home in front of fewer than three people. However, I have not seen any source say this explicitly (and I would expect Rav Getzel Ellinson in Woman and the Mitzvot to quote such a source, since he tries to include every opinion - see (b) below)
(b) The Gemara on Brachot 24a says that when a handbreadth of one's wife skin in a normally-covered place is revealed, one cannot say Shema (incidentally, the Gemara there notes that one may not gaze at even the little finger of a woman other than one's wife if one's intention is to derive pleasure). The Rosh there (#37) quotes the Gemara, and the Divrei Chamudot (#116, Rav Yom Tov Lipman Heller, the Tosafot Yom Tov) says that the prohibition is due to being normally covered, and any part of the body which is normally uncovered is not a problem. Rav Getzel Ellinson (Woman and the Mitzvot II p.210) quotes the Ben Ish Chai as holding the same view (with respect to a nursing woman). According to this opinion, if the custom in a given community is for even married woman not to cover their hair at home even when non-relatives are present, then there is no problem in saying Shema (or Kiddush, or any other prayer) in their presence, since men are used to it. Given that, there would apparently be no obligation based on lifnei iver for the women to cover their hair since (see below).
Approach (a) is problematic, because many explicit Gemaras forbid a man to look at women - for example, Bava Batra 57b which describes a man who intentionally takes a path which will lead by women washing clothes by the river (barefoot and bare-calved -- Rashbam) as wicked, and Brachot 24a mentioned above (incidentally, the Mishna Brura OC 75 #7 explains that only staring/gazing is forbidden when a woman is properly dressed, while even an incidental glance is forbidden if she is not). Given the prohibition of lifnei iver, putting a stumbling block in front of the blind (in this week's parsha, Kedoshim, as I write this in 5776!), is understood in many places in the Gemara (see Toldot Aharon to Vayikra 19:14) to mean one is obligated not to cause another to sin, how could a woman be allowed to dress in a way which would cause a man who sees her to sin?
Indeed we would should find an explicit prohibition in the Shulchan Aruch - just as we find we must refrain from selling certain things to non-Jews if they are likely to use them for idolatry (YD 151:1). Where would we expect to find that halacha? Not in EH 115, which discusses which behavior justifies divorcing a wife with prejudice, and not in OC 75, which discusses saying Shema when faced with immodest dress, but in EH 21, which says something (perhaps) surprising: "Jewish women may not walk in the market with uncovered hair..." - implying that at home they need not cover.
Approach (a) does not answer how she can avoid lifnei iver, but perhaps we can suggest that no man is obligated to see her in her private home, since he can always leave! Therefore she is not transgressing lifnei iver.
Approach (b) of course assumes that such behavior is commonplace in that community, and therefore men are accustomed to see womens' hair indoors, even though they are explicitly forbidden from showing hair in public; while such a private/public distinction seems difficult to justify, all opinions agree that we differentiate between the hair of married and unmarried women.
A problem with approach (b): if all rules of modesty are dependent on common practice and societal context, how can the Gemara in Ketubot 72a define lack of modesty? A possible solution: Brachot 24a only deals with what is arousing, which depends on context (like the Tosafot Yom Tov), and would be under lifnei iver. Ketubot 72a deals with violations of modesty, which is a divorce-able offense - not only lifnei iver, but (appropriately perhaps) kedoshim tihyu ("be holy!" - Vayikra 19:2) either defined by Chazal (like the Har Zvi) or mi d'Oraita like the straightforward implication there, but either way obligates a woman to absolute minima of modesty. If that is the case, then (b) is not an answer to the question, because the Divrei Chamudot only deals with when it is permissible to say Shema, or potentially lifnei iver, but not standards of modesty. Interestingly, Rav Ellison notes that Rav Ovadia Yosef in Yabia Omer says the Divrei Chamudot only applies to parts of the body beyond the minimum standards of modesty, but Rav Ellison says no such distinction appears in the Divrei Chamudot. It would appear that Rav Ovadia is understanding that the Divrei Chamudot must fit with Ketubot 72a (which the Tosafot Yom Tov surely knows about) and therefore limits his scope; Rav Ellison seems to have missed this point.
If this is the case, we need to understand why the Shulchan Aruch's obligation on women to cover their hair (EH 21:2) only mentions public spaces - perhaps because the idea that a woman would appear in front of unrelated men in her home did not occur to Chazal or the poskim.