I am not sure if you mean the UK Royal Family? (Sorry if I missed that point.) However - if you do - you can write to the Archivist at Windsor Castle.
They keep most of the records at Windsor Castle and the Archivist is very helpful. You do have to write an "old fashioned" letter though, and be patient for the reply!
Here is the address:
The Royal Archives
Berkshire SL4 1NJ
Give them as much information as you can, dates etc and they will reply, albeit slowly - and in a very smart envelope!
PS Some Royal records are at Kew, but I had a similar question to yours and the answer was at Windsor so it's worth a try.