بسم الله الرحمن الرحيم
The scholars of fiqh have explicated that it is unlawful for women to undertake a long journey without the company of male mahram. Therefore in the case mentioned above, your wife is not allowed to travel alone to South Africa.
(2-3) The exigent and emergence cases are exempted, but there is no such case here which may be called ‘exigent compulsion’.
Allah knows Best!
Darul Uloom Deoband