Can I retain General Status for my children if I Get married to an OBC

Once your cousin is married she will come under the category of an OBC but she cannot take the benefit of reservation for OBC by virtue of inter caste  marriage. 

Now regarding your second query,

The children at the time of birth will have the category of the father i.e. OBC in your case,so once a child is  born they will automatically come under the OBC category. 

Therefore in case of your cousin if she desires she may not apply for OBC certificate, but for her children she can apply for certificate only if she desires to take benefit of OBC category.