What is the ruling of Islamic law concerning a man who refuses to marry after the death of his wife, whom he loved very much, believing that this is better from a religious perspective, and she left him two young daughters?

It is best for a man to marry after the death of his wife, for it helps preserve his religion, keeps him chaste, and meets his children's need for care. It holds many benefits for the individual and society, and marriage is the Sunnah (definition) of the Prophets. It is not true that refraining from marriage is a sign of loyalty to the deceased wife. The Prophet, peace and blessings be upon him, married after the death of Khadijah, and the Companions married after the death of their wives, and Imam Ahmad married after the death of his children's mother.