All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for a husband if he travels and the like to leave his wife with a Muslim family that he trusts.
However, a woman is obliged to abide by the religious requirements, like not allowing a non-Mahram to be in seclusion with her or revealing her adornment in front of him, and the like.
Finally, it should be noted that if a husband wants to travel, he is not permitted to leave his wife in a condition where she might be exposed to evil and corruption; he should either take her with him or leave her in a safe place.
Allaah Knows best.