Is it permissible to marry a widow who has offered herself for marriage with a specified dowry to preserve her chastity and raise her children?

You have not mentioned the wording of the contract, nor the presence of a guardian (wali) and witnesses. If the contract fulfilled the conditions of validity, with a guardian and witnesses, and was phrased as a gift in exchange for the mahr (dowry), then its ruling is explained in Fatwa (definition): 68406. However, if the conditions were not met, then it is invalid, due to the saying of the Prophet, peace and blessings be upon him: "Any woman who marries without the permission of her guardian, her marriage is invalid," and "There is no marriage except with a guardian and two just witnesses. Any marriage that is otherwise is invalid."