Good point that ה is the definite article "the," but idiomatically in Hebrew when they add a possessive pronoun (his, her, their), which is שׁל then they put in the definite article also. However, someone responded that sometimes the definite article is left out and it seems to be OK. So both are ok apparently.
It's not a matter of sometimes leave it out & sometimes include it. You omit the definite article ה only for certain special close people : father, mother, sister, brother. I'm not a native speaker -- just going by what DL gave at the beginning of the section-- but I imagine Grandma and Grandpa would also be included in this special group of words.
Partitive mem: I think it would be אחד מהתפוזים שלו. (+ טעים of course at the end.) At first I thought we would need the construct sg in this case, which has the same consonants but the nikkud are different: אַחַד instead of אֶחָד. However, the construct state isn't needed with partative mem, as in 1 Sam 16:18 וַיַּעַן֩ אֶחָ֙ד מֵהַנְּעָרִ֜ים, "one of the young men answered." E.g., חלק מהספרים, "some of the books."