I'm not sure what you mean -- "I am your grandchild" is not a correct translation of Ich bin sein Enkel.
It means "I am his grandchild" or "I am his grandson", not "your".
Also, Enkelin is specifically a granddaughter, while Enkel can be either a specifically male grandchild (a grandson) or a grandchild in general, sex unspecified -- especially in the plural.
Enkelsohn and Enkeltochter are a specifically-gendered pair of words.
The difference between sein, seine and ihr, ihre is basically like "his" and "her" in English.
sein Onkel is "his uncle", ihr Onkel is "her uncle. seine Tante is "his aunt", ihre Tante is "her aunt".
So the base word (sein-, ihr-) "his, her" depends on the gender of the owner; the ending depends on the gender of the "possession" (-e for a feminine or plural noun, no ending for a masculine or neuter noun).
Ich bin ihr Enkel would be "I am her grandson".
And Ich bin ihre Enkel would be "I am her grandsons" or possibly "I am her grandchildren" -- since Enkel is grammatically masculine, the -e ending on ihre must indicate that the noun Enkel is plural here. (The word has the same shape in the plural as in the singular.)
Ich bin sein enkel. How do I know who the enkel is referring to Großmutter or Großvater.
sein is the possessive determiner related to er or es.
So it can only refer to the masculine Großvater, not to the feminine Großmutter.
sein Enkel = his grandchild/grandson
"her grandchild/grandson" would be ihr Enkel.