I am a second wife from a marriage without permission. If we register it, my husband may be prosecuted. Should we keep quiet?

No; staying quiet prolongs the risk to you and your children, while the penalty is the price that must be paid to put things right. Without registration, your rights to maintenance and inheritance and your children's documents are always shaky. If your husband died suddenly, proving the marriage would become much harder. Discuss with your husband that correcting a mistake is better than waiting for it to come to light. Get advice from a syarie lawyer about the procedure in your state, including registration and validation of the marriage. Be prepared too for the first wife to find out; that is part of an honesty long overdue. See if the husband dies before registration.