Saying “Allahummaghfirli warhamni wahdini warzuqni” between the Two Prostrations
Question

What is the ruling on saying “Rabb ighfir li wa li walidayya (Lord forgive me and my parents)” when sitting between the two prostrations? Is that permissible?.
Praise be to Allah.Reported du`a between the two prostrations 
You should adhere to what was narrated of the du`a of the Prophet (blessings and peace of Allah be upon him) between the two prostrations, which is to say, “Rabb ighfir li (Lord forgive me)”, as it was narrated by an-Nasai (1145) and Ibn Majah (897) from Hudhayfah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations: “Rabb ighfir li, Rabb ighfir li  (Lord forgive me, Lord forgive me).” 
The Prophet (blessings and peace of Allah be upon him) also used to say between the two prostrations : “Allahumma ighfir li warhamni wajburni warfa‘ni wahdini wa ‘afini warzuqni (O Allah, forgive me, have mercy on me, console me, raise me in status, guide me, grant me well being  and grant me provision).” 
At-Tirmidhi (284) narrated from Ibn 'Abbas (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations : “Allahumma ighfir li warhamni wajburni wahdini warzuqni (O Allah, forgive me, have mercy on me, console me, guide me, and grant me provision).” 
Abu Dawud (850) narrated it as follows: “Allahumma ighfir li warhamni wa ‘afini wahdini warzuqni (O Allah, forgive me, have mercy on me, grant me well being, guide me and grant me provision).” 
Ibn Majah (898) narrated it as follows: “Rabb ighfir li warhamni wajburni warzuqni warfa‘ni (O Lord, forgive me, have mercy on me, console me, grant me provision and raise me in status). 
This hadith was classed as authentic by al-Albani in Sahih at-Tirmidhi. 
An-Nawawi (may Allah have mercy on him) said in al-Majmu‘ (3/414):
“With regard to the hadith of Ibn 'Abbas, it was narrated by Abu Dawud, at-Tirmidhi and others with a good chain of transmission . It was narrated by al-Hakim in al-Mustadrak and he said: Its chain of transmission is authentic. He quoted the different versions then he said: To be on the safe side, the best option is to combine all the reports and say all the phrases mentioned, of which there are seven: “Allahumma ighfir li warhamni wa ‘afini wajburni warfa‘ni wahdini warzuqni (O Allah, forgive me, have mercy on me, grant me well-being, console me, raise me in status, guide me and grant me provision).” 
Can you add to this formula “Allahummaghfirli warhamni wahdini warzuqni”?
With regard to adding to this du`a, what appears to be the case is that it is permissible, but it is preferable to keep to what has been narrated and to offer du`a for one’s parents in prostration or before saying the salam at the end of the prayer. Muslim (479) narrated from Ibn ‘Abbas (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “…as for prostrating, strive in du’a, for it is deserving of a response (from your Lord).” 
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“Then he should rise from prostration, saying “Allahu akbar (Allah is most great),” and sit muftarishan, which means sitting on the left foot and holding the right foot upright, placing his right hand on his right thigh or on his knee, extending his fingers over his knee, and placing his left hand on his left thigh or his left knee, extending his fingers over it. This is the Sunnah. And he should say: “Rabb ighfir li, Rabb ighfir li, Rabb ighfir li (Lord forgive me, Lord forgive me, Lord forgive me), as the Messenger (blessings and peace of Allah be upon him) used to do. And it is mustahabb to say in addition to that: Allahumma ighfir li warhamni wahdini wajburni warzuqni wa ‘afini (O Allah, forgive me, have mercy on me, guide me, console me, grant me provision and grant me well-being), because that is proven from the Prophet (blessings and peace of Allah be upon him). And if he says more than that, there is nothing wrong with it, such as if he says, “Allahumma ighfir li wa li walidayya (O Allah, forgive me and my parents)” or “Allaahumma adkhilni al-Jannah wa anjini min an-nar (O Allah, admit me to Paradise and save me from Hell)” or “Allahumma aslih qalbi wa ‘amali (O Allah, make my heart and my actions righteous) and so on. But he should ask a great deal for forgiveness between the two prostrations, as was narrated from the Prophet (blessings and peace of Allah be upon him).” (Fatawa ash-Shaykh Ibn Baz, 11/36) 
And Allah knows best.