Imam al-Shafi'i (may Allah have mercy on him) said: "A hadith has been narrated about this, even though it is among those reports whose like is not established."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / Q14087
Sayyiduna Abu Sa'id (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) said: "When one of you comes to his wife and then wishes to return (to her), let him perform ablution."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14087
Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with him) narrates from the Prophet (peace and blessings be upon him): "When one of you wishes to return to his wife again, let him perform ablution, for it makes him more energetic."
If al-Shafi'i (may Allah have mercy on him) meant this hadith, then its chain is sahih (authentic); perhaps he did not come across its chain.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14088
Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) said that the Messenger of Allah (peace and blessings be upon him) said: "When you come to your wife and wish to go back again, perform ablution as you do for prayer."
This is how al-Musayyab bin Wadih narrated it, and it is not mahfuz (preserved).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14089
Sayyiduna Umar (may Allah be pleased with him) narrates from the Prophet (peace and blessings be upon him) that the Prophet (peace and blessings be upon him) said: "When one of you comes to his wife and wishes to return, let him wash his private part."
This is more correct, though Layth bin Abi Sulaym is not used as evidence, and the hadith of Abu Sa'id suffices. A hadith has also been narrated about taking a ritual bath in between, but it is not strong.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14090
Sayyiduna Abu Rafi' (may Allah be pleased with him) said that the Prophet (peace and blessings be upon him) went round to all his wives together and took a ritual bath with each one of them. I said: "O Messenger of Allah, why did you not make it a single one?" He (peace and blessings be upon him) said: "This is cleaner, purer and better."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14091