بسم الله الرحمن الرحيم
(Fatwa: 149/108/L=02/1435)
After having sex with wife, it is lawful to have a second intercourse even without wudhu or ghusl, but it is better to do ghusl, or do wudhu or at least wash the private parts.
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband
