Is it permissible for a woman whose husband has passed away to go out during the day to visit her children and return to her home for the night?

The basic principle is that it is impermissible for a woman observing 'iddah (waiting period) to leave her home, except out of necessity. It is permissible for her to visit her young children if they are in need of her, provided she abstains from adornment and does not spend the night anywhere but in her own home.