Washing of legs is wrong as you heard it. In Hadith, it is mentioned that at the wedding night the husband should recite the below dua holding his wife’s forehead hair:
اللھم انی أسئلک من خیرھا و خیر ما جبلتھا علیہ و أعوذبک من شرھا و شر ما جبلتھا علیہ
Then he should offer two rakat salah as token of thanks with husband standing ahead of wife. After salah they should pray for mutual love, blessings of Allah, unity and prosperity.
It is stated in Ghunyatut Talibeen that they should clean themselves from impurity after intercourse. If he wishes to do intercourse again he should at least make wuzu otherwise it is better to bath. However, he has to do bath before Fajr salah so that he can perform it timely. It is a grave sin to miss salah due to laziness.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband