Is it permissible to perform tayammum instead of ghusl to purify oneself from ritual impurity (janabah) due to embarrassment from frequent bathing in front of the husband's family, knowing that this tayammum would only be once or twice a week?

One must perform ghusl (ritual bathing) from janabah (state of ritual impurity requiring ghusl) with water. It is not permissible to resort to tayammum (dry ablution) except when the use of water is impossible, either due to its unavailability or harm from using it, based on Allah’s Almighty statement: (And if you are in a state of janabah, then purify yourselves) [Quran 5:6], and the Prophet’s (peace be upon him) saying: "Clean earth is the ablution for a Muslim, even if he does not find water for ten years. But if he finds water, then let him fear Allah and let him touch his skin with it, for that is better." It is not permissible to abandon ghusl due to shyness. Tayammum is not sufficient in such a case, and the prayer will not be valid. Shyness that leads to abandoning obligations is blameworthy. It is possible to perform ghusl at times when others will not be aware, or to use water in a way that no sound is heard.