This is the "ordinary" use of will to signify future reference, backshifted into the past-tense form because the 'future' being spoken of is future with respect to a point in the past.
If that's too hard to follow, look at it this way:
If she were experiencing hope now, in the present, we would say:
She hopesPRESENT-TENSE FORM for a future when marriage willPRESENT-TENSE FORM not have to end a career of research.
But we are talking about her experiencing hope at some time in the past, so we 'backshift' the present-tense forms into past-tense forms.
She hopedPAST-TENSE FORM for a future when marriage wouldPAST-TENSE FORM not have to end a career of research.
As for have to with would: you cannot use modals like 'must' this way, because they don't have the necessary infinitive form to combine with would. But one reason why have to is now replacing must is precisely because have does have an infinitive (and other non-finite forms), so it permits this use. Have is not being used syntactically as an auxiliary, even though it has a modal sense, but as a lexical verb.