What is the ruling on giving a sum of money to a newborn when visiting them, and what is the ruling on not returning it? Is giving a gift better?

There is no objection to giving gifts to a woman on the occasion of childbirth, whether money or otherwise. The Shari'ah encourages the exchange of gifts and cooperation due to their beneficial effects in removing resentment, affirming affection, and instilling love. As for returning a gift, it depends on the local custom and tradition. Rewarding the giver is among the noble morals, as the Prophet, peace and blessings be upon him, used to reward and reciprocate gifts.