My dad's brother in Holland passed away leaving an inheritance to his next of kin. Since my dad is deceased this passes to my sister and myself. They are asking for proof of his death which I assume is his death certificate. They are also asking for proof that we are his only children...what type of legal document would I need to proof that?
Start with your birth certificates.
Since it's Holland, you have to find out what they want. Birth certificates may be enough, but they may want a court order. If they do, hire a lawyer to file a petition to determine heirship under Family Code section 248.