Is it wrong to marry a man who is already married and has three children without informing his wife, but with the knowledge and approval of his family and my family after much insistence from my side?

It is not a flaw for a woman to marry a married man, and no consideration should be given to customs that deem this a flaw, as such customs contradict the Sharia which permits polygyny due to the benefits it entails. That which is permissible by Sharia involves no harm. Harm only occurs if one attempts to turn the husband away from his first wife or demands her divorce. If the first wife is distressed by her husband's marriage, then the second wife is distressed by his not marrying her, and the first wife is not more deserving of consideration.