Mugabe is said to have assaulted Gabriella in the Capital 20 West Hotel in Sandton with an electric extension cord last Sunday.
"The DA will be demanding an immediate parliamentary inquiry into (the) government's complicity in allowing Zimbabwean First Lady Grace Mugabe to flee the country in the dead of night to avoid criminal prosecution", DA whip John Steenhuisen said in a statement.
South African police had previously issued a red alert at borders to ensure she did not leave undetected and had said they were waiting for a government decision on the immunity appeal. "She is not somebody who has been running away", Mbalula said, according to South Africa's News24.
Zimbabwe First Lady Grace Mugabe recently traveled to South Africa, reportedly to address issues with her two sons, Robert and Chatunga. "She hit my daughter with a plug socket", Engels told Reuters. But Grace Mugabe had not been seen since the allegations were made and failed to appear at the Pretoria summit.
The lawyers did not reveal the amount offered.
Afriforum, an Afrikaans rights group that Nel joined in January after quitting as a state prosecutor, said it would be illegal for Pretoria to give Mugabe immunity and branded the plans a "disgrace". Her crime was for "hanging out" with her two sons who school in the country.
The rumours that Ms Mugabe is about to be let off the hook have caused uproar among South Africans, who have become exhausted of seeing politically connected people escape justice because of whom they know.
The 52-year-old, who has not yet been charged, has asked for diplomatic immunity in the case.
She's yet to be granted immunity.
In a move to try to defuse the situation, South Africa's Department of International Relations and Co-operation insisted on Friday that no decision had been taken yet on Ms Mugabe's application for diplomatic immunity. It won't apply if she's here on holiday or for something else.
"The other difficulty she would have is that these individuals are required to be registered by the minister of foreign affairs in the Government Gazette, which has to be published". But, it also may have given South African authorities additional time to consider a diplomatic immunity request that had been delivered from Mrs. Mugabe.
Spies said they will approach the court if Mugabe is granted immunity‚ because they believe her claim she was accompanying her husband Robert to a SADC summit in South Africa was an "afterthought".
Grace has in the past been caught in incidents of violence. In 2009, a newspaper photographer in Hong Kong said she and her bodyguard had assaulted him.