What is the ruling of Islamic law regarding the unmarried sister of the husband interfering in all personal matters of the wife, and does Islamic law oblige the couple to take her with them when they travel and go out for recreation?

Lying is forbidden and considered a major sin, but it is permissible out of necessity if it is the only way to avert hardship, provided it does not infringe upon the rights of others. It is preferable to use ma'areed (equivocation), which involves speaking words that the listener understands in one way, while the speaker intends another meaning, like the example cited by Sheikh Al-Islam.

As for the second part of the question, the husband is not obligated to take his sister with him when traveling or going out for recreation. He may do so if he wishes, but he must not neglect his wife's right, such as cohabitation (wat'). There is no harm in the sister sleeping in the same room with her brother and his wife, provided there is modesty and that the couple has a private space when engaging in intimacy.