Is it permissible to marry عرفيًا (customarily/unofficially) and verbally without announcement after a verbal divorce and subsequent verbal reconciliation, and is it permissible to marry secretly the one you love out of fear for the children?

If the divorce was revocable and not documented in courts, then your husband took you back before the 'iddah (waiting period) ended, the reconciliation is valid, and you remain his wife. It is not permissible for you to marry another as long as you are under his marital bond, and if that occurs, your marriage is void. If your husband abandons you, you have the right to demand marital relations in a reasonable manner. If he does not comply, you may refer his case to the judiciary to compel him to do so or to divorce you. After the occurrence of divorce or khul' (divorce at the wife's instance) and the expiry of the 'iddah, there is no objection to your marriage to whomever you wish, through your guardian and with the presence of two witnesses. It should be noted that marrying another without terminating the first contract in court may lead to corruption and the loss of rights.