What is the source in Halacha for wearing a Tichel and when this should be done? I learned that ones hair must be completely covered at all times so why would wearing a Tichel in the street be not OK and at home it is OK? In short, when is a Tichel allowed and under what conditions?
Firstly, a Tichel is halachically fine as long as it covers all of the hair. The fact however is that this is rarely accomplished. Many a time, some of the hair is protruding from the Tichel. At times, there is a concern that a woman might move it back or even remove it completely.
This concern does not apply with a Shaitel. Even when none of these concerns apply, there is still an issue that others who are not at this level might learn from her behavior and wear a Tichel.
(This is especially the case in non Chareidi communities. Indeed in some Chareidi communities where the woman have large tichels that completely cover all of their hair; one cannot have any complaints against their custom.)
Therefore, many Poskim, including the Lubavitcher Rebbe, hold that a Shaitel (Tznius) is the correct – and even necessary – method in order to ensure that all hair is covered.
One must cover their hair both indoors at home and outdoors in the street. However, since the obligation to cover hair MiDeoireisa (Biblically) applies only outdoors, many are extra particular outdoors to wear a Shaitel and suffice with a Tichel indoors. Of course, the Tichel should be worn in such a way that it covers all strands of hair completely. As long as there are no guests at home it’s halachically acceptable to wear a fully Tznius Tichel at home.
Some are particular to cover their hair even at home with a Shaitel. This is commendable and they bring about extra blessings for themselves and for their entire family in all areas. Indeed, the implication and spirit of the Rebbe’s letters on the subject seem to inply that this is the correct behavior.
See Igros Kodesh vol. 9 p. 325; vol. 19 p. 428; vol. 10 p. 186; vol. 16 p. 330. Sefer Leket Shichechas Hapeah.