Is it a sin to have intercourse with one's wife secretly after she has separated from her husband due to pressure from his family, and must she seek a divorce because of this?

You are his wife, and you are still under his marital authority. Intercourse and other marital relations are permissible for you with him, as Allah the Almighty said: "It has been made permissible for you the night of fasting to approach your wives [for sexual relations]. They are clothing for you, and you are clothing for them."

You are not required to seek a divorce due to his inability to take you back. Nor is he religiously obligated to obey his parents in their command to divorce you, unless there is a legitimate religious reason.

The family's attempt to separate the spouses without a legitimate reason is a great injustice and sin, and it is the act of sorcerers and devils. Therefore, they should be advised to cease their actions.

If they do not respond, he may take you back even if they become angry, and by doing so, he would not be undutiful.

It is advised to make abundant supplications for Allah to facilitate the matter, and among these supplications is: "O Allah, there is no ease except in what You make easy, and You make the difficult easy if You wish."