And Helios, the Hyperion force, was climbing into his golden bowl, until having passed through Ocean he would come to the depths of dark and holy night, to his own children and their mother, his wedded wife. But the other, the child of Zeus, went by foot into the Laurel-shaded grove.
Ὑπεριονίδα <ἴ>ς – not “the force of Hyperion”, but rather “the force of Hyperionidas”, i.e., the Sun, who is the son of Hyperion. This is just an epic honorific formula for the name Hyperionidas, probably best translated as “Hyperionidas” tout court. Or you might try something like “Lord Hyperionides.” [Edit: I see I wrote Hyperion instead of Hyperionidas, falling into the same error as you.] -δα is Doric masculine genitive; Ὑπεριονίδας would be the Doric nominative; and the Attic/Ionic forms would be Ὑπεριονίδης/Ὑπεριονίδου.
ποτὶ ματέρα κουριδίαν τ᾽ ἄλοχον παῖδάς τε φίλους – “to his mother and his wedded wife and his dear/own children”. These are coordinate. While φίλος modifying a family member can sometimes be translated “own” in epic language, there’s no contrast here with someone else’s children, so I think “his dear children” would be better, or maybe “his own dear children”. This is an epic formula, and I don’t think here it’s absolutely devoid of affectionate connotation, especially in combination with mother and wife.
ὁ δ᾽ – while there may be a contrast here between the Sun and the Son, (Herakles, son of Zeus), I think “the other” is a little too strong. I would just translate δ᾽ as “but”.
Ἅλιος does not fit the metrical scheme and must be either intrusive or corrupt. It shouldn’t be translated. The other obelized places, on the other hand, have only a little something wrong with them (they’re not quite metrical), so they can be translated fairly harmlessly.
ὄφρα introduces a purpose clause, “so that, in order that.”