I don't understand why we can't visit my dad's grave until after the first yahrtzeit. My parents were married for 45 years, and my mom is understandably very sad, and would like to visit already.
I'm sorry to hear about your loss. May G‑d comfort you amongst the mourners of Zion and Jerusalem, and may you only know of happiness and simchas from here on.
I assume you are referring to the custom followed in certain communities that relatives do not visit their loved one's gravesite until one year after the passing.
You wonder about the reason for this restriction. In your email, though, you allude to the answer: "My mom is very sad." Going to the place where your dad is buried will likely not ease her sadness; it will make it worse. In turn, the sadness will make it difficult for your dad's soul to adapt to his new spiritual home. Going to his grave can pull his spirit back to This World and interfere with his acclimation.
However, this restriction is not a universal Jewish custom. In some communities it is considered perfectly acceptable to visit a grave at any time.
So my advice is, speak to your rabbi to determine your particular family/community tradition in this regard. Also discuss with your rabbi (or maybe with a mental health professional) whether it is psychologically prudent for your mother to visit the grave so soon.