What is the ruling on having intercourse on the day and night of Eid (my question includes both Eids)? I heard from some sincere brothers that it is not permissible.
What you have heard from some sincere brothers is not correct. Intercourse on the night and day of Eid is permissible, and it is not haraam to have intercourse except during the day in Ramadaan and when in the state of ihraam for Hajj and ‘Umrah, and when the woman is menstruating or bleeding after childbirth (nifaas).
And Allaah knows best.