For months the woman's family has not answered our proposal. Should we ask?

Yes; asking politely is your right, and it helps both sides out of a state of limbo. Let a family representative contact them, not the man directly contacting the young woman. Use words that do not pressure, for example: ‘We are just asking after our earlier intention. If the family needs more time, we understand.’ If the answer is still vague, you may set a time limit kindly. Prolonged silence is sometimes how some families refuse without saying so directly. Accept whatever the answer is with an open heart, and get on with life without bearing a grudge. See when a proposal is declined.