You can't. It's ambiguous. That's why either translation is accepted.
One of the currently accepted translations is "They will offer her House". Is this acceptable English without the article? And is it really possible to understand the German sentence in this way (again, without the article)?
EDIT: Okay... this was just me being dumb. Somehow the possessive meaning of "ihr"/"her" did not register at all, and I was just trying to somehow forcefully fit in "ihr" = "to her".
"Sie werden ihr Haus angeboten
werden" (anbieten is passive in sentence, not werden). However I don't know whether the passive can be used that way in German (that is, to make the indirect object into a subject). "Ihr Haus wird Ihnen angeboten werden" instead is definitely correct.
Again, not in that form: the second "werden" doesn't need to be perfect participle, it has to be infinitive (because that is how you make the future in German: werden + infinitive). So "Sie werden ihr Haus angeboten
werden" is the correct form. Also, and I notice it just now, there is no need to capitalise "ihr".
(Again, someone else will have to tell whether the sentence is correct in its entirety, but the last "geworden" is definitely incorrect and needs to be werden)