Does the second wife have the right to demand her husband spend the the night with her if she went to her family's house of her own free will?

The husband must be just among his wives in nightly lodging, unless there is a reason that overrides this, such as the wife's disobedience (nushooz). If the duration of stay is short and there is no harm in you remaining with your family, it might be better not to instigate a disagreement with the husband over this matter. There are disagreements among jurists regarding the duration of equal division among wives. Some prohibit exceeding one day and one night unless with the consent of the other wife, while others permit division for up to three nights or a week, always considering the consent of the other wife in all cases.