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These issues are easily rectified with supporing documents.
Your wife should provide a divorce certificate. It is a bit strange your range of skills but that is not a ground for refusal. You need to provide employment letters of both employment. You also need to provide your qualification documents. You also need to ask the school your children go to to give a letter of reference.
Your wife also needs to provide evidence of employment with income of £18,600.
OK. Is your wife settled in the UK. What I mean is does she live and work in the UK?
OK. Can you confirm if your children are British citizens and what your wife's income is
I am still waiting for your response.
OK. This was the first time you mentioned your children are British. Being UK born does not give automatic entitlement to British citizenship.
Now I see the reason your application failed is because your wife who is your sponsor did not meet the financial requirement. Your sponsor must earn at least £18,600 pa. She earns £12,000 pa. The reference from your children's school should confirm they are registered, enrolled and attend at the said school.
The financial requirement is not about your income, its main focus is on your wife's income. I am aware that there have been some changes allowing third party support and other means to meet the financial requirements but this type of assessment cannot be done here.
Remind me what application did you submit
OK that changes things as from reading your initial question it sounded like you made a spouse visa. With a visitors visa I am guessing the visa was refused because it wasn't believed you would return back home because you have a stronger tie to the UK than you have in SA.
It may be necessary to instruct a lawyer to assist you in making a further application.
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