Cremation is fine for Christians, and the Bible doesn’t forbid it anywhere. Burial was the common practice in Scripture, but that was custom, not a command.
Genesis 3:19 says we return to dust either way. And think about believers lost at sea or martyrs burned at the stake. The God who made Adam from dirt can handle ashes. Paul describes the resurrection body as a new thing (1 Corinthians 15), like a seed becoming a plant (see this thread).
On your family member, their concern comes from a good place. The resurrection is God’s miracle, and it doesn’t depend on how well our remains are preserved.
Make the choice that fits your conscience and your budget.