You will need to have your grandfather's marriage certificate .I do not know from which nation you hail, but in the United States, to obtain your grandfather's marriage certificate, you must call or visit the city's department of vital records ;i.e, the city in which your grandfather was married. Even if you do not know exact dates, they will help you find the date and the certificate by using the other vital information you provide them about your grandfather. In addition,, if he was divorced you will need the divorce decree too.
Regarding your mother; yes, I believe if she is divorced you must include the divorce certificate since she is the parental citizen through whom you are applying for Foreign Birth registration.
Another way to find out the date of your grandfather's wedding is to contact the church where the wedding took place I am sure your mother will have those records. Believe it or not churches keep records from the 1940's and further back. You may NOT use the marriage certificate from the church as his marriage certificate-you must have a certified copy from the city, but you may use the data on it to help with the city' search for the certificate and the process of obtaining it will be a lot quicker. I did this. Funny how family secrets/skeletons come out in this process isn't it?