Is It Permissible to Live Separately to Protect My Children's Islamic Upbringing?

If the situation is truly as described in the question, and there are no additional details that would change the ruling, then seeking a separate living arrangement or maintaining appropriate boundaries solely to protect your daughters' Islamic and moral upbringing is not, in itself, sinful. Parents have a duty to safeguard their children's faith, modesty, and character. Therefore, if there is a genuine concern that a particular environment may negatively influence their upbringing, it is permissible to take reasonable steps to protect them, provided this does not involve injustice, mistreatment, or severing family ties.

Accordingly, if your intention is only to protect your children's upbringing not to humiliate your sister-in-law or cut off family relations then, in principle, requesting separate accommodation or maintaining appropriate boundaries is permissible. At the same time, you should continue to treat your sister-in-law with kindness and respect, uphold family ties, and, where appropriate, advise her gently and wisely about the importance of modesty.