Should DNA be carried out on a child with or without the knowledge of the wife (mother of the child)?

My advice would be to take the test secretly. If you have serious reasons to believe that such test is needed, you should not have told her it anyway. It is a difficult situation, because, on one hand, such suggestion can be very unpleasant to her, because it directly implies at mistrust towards her and can be quite insulting.
Anyway, your interests must come first for you. If it is important for you to be sure that you are not being cheated, you must take the test secretly.
If the test results reveal that one or more of your children are actually not your children, it is extremely important that you don’t do or tell anything, anything at all without prior consultations with the trained lawyer. Always approach a good legal advice before you make any decision, and don’t be afraid to appear ruthless, it is much better to be ruthless than let someone else treat you ruthlessly.
Do whatever you possibly can to prepare yourself for divorce, try to protect your income and property as much as you can and actually, investigate options to gain as much as possible from the divorce, and make her pay as much as it is realistically possible in your specific case.
The same goes for your behavior – avoid any actions which could be interpreted against your interests, and gather any evidence which you will possibly work in your favor.