Does the superiority of a woman's prayer in her home cease if she does not find devotion in prayer due to family problems, while she finds it in the mosque, to which she sometimes goes alone?

A woman's prayer in her home is superior, and it is permissible for her to go to the mosque for Tarawih prayers and others, provided certain conditions are met. If a woman cannot achieve khushu' (devotional humility) in her home, then praying in the mosque is better for her, provided there is no fitnah (temptation/strife) or suspicion. A Muslim woman must invite her family and relatives to return to Allah, repent from sins, and engage in da'wah (inviting to Islam) with those who are receptive, being gentle in her invitation and choosing appropriate times.