Is the marriage of a woman to a family friend after she requests a divorce (khulʿ) and intends to marry him before the divorce is finalized valid in Islamic law, and what is the ruling after she has given birth to two children?

A woman's agreement with a man to marry before she obtains a khul' (divorce initiated by the wife) from her husband and before her waiting period (iddah) expires is forbidden, and both of them must repent.

If the marriage contract was concluded, fulfilling all its conditions, after the waiting period expired, then it is valid and does not need to be renewed. However, if it was concluded before the waiting period expired, it is invalid by the consensus of the scholars, based on the Almighty's saying: (And do not determine to solemnize a contract of marriage until the prescribed period has reached its end) [Al-Baqarah: 235]. In this case, they must renew the contract and repent.