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Vital records are generally created and held at the town, county, and/or state level, not at the federal level.
Depending on the state and its laws regarding vital records, you may just be able to request their birth certificates, or you may have to provide proof as to your relationship to your mother and grandmother in order to be eligible to receive copies of their birth certificates. For example, in California, most vital records are considered public record and anyone can receive informational copies (identification requirements exist for getting copies that can be used to prove identity - source); records can be requested from either the county or the state. On the other hand, in Kansas, vital records are not considered public record and you must provide proof of relationship in order to request and receive those records (source); records mid-1911 and later can only be requested from the state. There are also some places that have other oddities - for example, New York State does not maintain vital records for New York City (source).
Finally, depending on when your mother and grandmother were born and where (and whether their parents bothered reporting the birth), there may just not be a birth record. For example, of my grandfather and his approximately 14 siblings, born between 1885 and 1915 in Kansas, I have only found one (b. 1892) that has an actual birth record, and I have yet to find delayed birth records for the rest.