That's Not Your Daughter's Name!
If you want to know the correct pronunciation of your granddaughter's name, I'll be happy to tell you. It's whatever her parents say it is, of course. They named her, and they know perfectly well what name they chose.
Now, if your question is how to pronounce the name spelled A-I-D-A, that's a different matter. The Ethiopian princess Aida who is the heroine of Verdi's opera (and Elton John's Broadway musical) is pronounced as three syllables: eye-EE-da. Anyone with a passing knowledge of opera will usually read it that way.
That's not the only possible origin or pronunciation for those four simple letters, though. Across the generations, there have always been smatterings of women named Aida as an alternate spelling of Ida or Ada. The Ada pronunciation has been picking up steam lately, as parents seem to see Aida as a feminine version of Aidan.
Since the Ida pronunciation is the least common of the three, I'm afraid your granddaughter is facing a lifetime of correcting people. When you first heard the name, you might have gotten away with politely pointing that out: "Oh, it's so lovely but I'm worried the spelling will mislead people and they'll get her beautiful name wrong!" But I'm afraid it's too late for that. Now that you've treated your daughter-in-law like she doesn't know her own child's name ("constantly" being corrected??), there's nothing left but to make nice. A baby blanket embroidered AIDA would be a good start.