Hi Marwatone,
let me make you correct. Hazrat Ali did not get marry in the presence of Hazrat Fatima bint e Muhammad (PBUH). after the death of Hazrat Fatima the brother of Hazrat Ali, Hazrat Aqeel, introduced a lady whose name was also Fatima and Famous as Hazrat Fatima bint e Asad, and asked him to get marry with her Hazrat Ali accepted the proposal of his brother and got marry with Hazrat Fatima bint e Asad who is the second wife of Hazrat Ali and Hazrat Abbas is the son of his Second wife, Hazrat Fatima bint e Asad.