Prayer in congregation in the mosque is obligatory for men according to the more correct of the two scholarly opinions, because of a great deal of evidence to that effect, which has been quoted in the answer to question no. 120.
Taraweeh prayer is a confirmed Sunnah (Sunnah mu’akkadah), and men should offer it in congregation in the mosque. This has been explained in the answer to question no. 45781.
It is better for a woman to pray in her home than in the mosque, because the Prophet (peace and blessings of Allaah be upon him) said: “Do not prevent your womenfolk from coming to the mosques, although their houses are better for them.” Narrated by Abu Dawood (567); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
And the Prophet (peace and blessings of Allaah be upon him) said: “A woman’s prayer in her house is better than her prayer in her yard, and her prayer in her chamber is better than her prayer in her house.” Narrated by Abu Dawood (570); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
This is general in meaning and includes Taraweeh prayer and other prayers. Please see question no. 3457.
Based on this, what your husband did is strange, because he forsook an obligatory duty, which is praying ‘Isha’ in congregation in the mosque, then he forsook a Sunnah which should not be neglected, namely praying Taraweeh in congregation in the mosque. All of that was so that you could do something that at the most is permissible and is not obligatory or mustahabb.
But perhaps he does not know that it is obligatory to pray in congregation, and he did that to honour you. May Allaah reward him with good for his kind treatment of you, but he should not do that again in the future. He can treat you kindly by enabling you to pray at home and keeping distractions from the children etc away from you.
We ask Allaah to guide us and you.
And Allaah knows best.