Praise be to Allah.
What you have heard about intercourse not being allowed when seeing the new moon at the beginning of the month is not correct, and we do not know of any hadeeth concerning that. It is permissible for a man to have intercourse with his wife at any time, except when one of them is in ihraam for Hajj or ‘Umrah, or is fasting, so it is not allowed during the day when one of them is fasting, but it is allowed at night; it is also haraam when the woman is menstruating or bleeding following childbirth.
Allah says (interpretation of the meaning):
“The Hajj (pilgrimage) is (in) the well-known (lunar year) months (i.e. the 10th month, the 11th month and the first ten days of the 12th month of the Islamic calendar, i.e. two months and ten days). So whosoever intends to perform Hajj therein (by assuming Ihraam), then he should not have sexual relations (with his wife), nor commit sin, nor dispute unjustly during the Hajj” [Al-Baqarah 2:197]
“It is made lawful for you to have sexual relations with your wives on the night of As-Sawm (the fasts). They are Libaas [i.e. body-cover, or screen, or Sakan (i.e. you enjoy the pleasure of living with them)] for you and you are the same for them” [Al-Baqarah 2:187]
“They ask you concerning menstruation. Say: that is an Adha (a harmful thing for a husband to have a sexual intercourse with his wife while she is having her menses), therefore, keep away from women during menses and go not unto them till they are purified (from menses and have taken a bath). And when they have purified themselves, then go in unto them as Allah has ordained for you (go in unto them in any manner as long as it is in their vagina). Truly, Allah loves those who turn unto Him in repentance and loves those who purify themselves (by taking a bath and cleaning and washing thoroughly their private parts and bodies for their prayers)” [Al-Baqarah 2:222]
And Allah knows best.