they may not retain the general caste and they will have to go by the caste of their father.

I do not agree with the above opinion. One is required to declare himself as a S.C. ONLY for claiming benefits available under 'reservation' schemes of the Government. Otherwise, if a benefit under reserved category is not to be claimed, anybody can claim himself belonging to 'general' category.

Your children may, if you or they so desire, even keep your last (family) name of your father as their last name. Alternatively, they do not need to enter the caste bandwagon at all and may be kept away from this system.

You should keep in mind that for claiming benefits under SC category, one may require a certificate as proof of caste. If that certificate is not required to be produced for claiming benefits, there is no requirement of proving your caste anywhere.