Is it obligatory to fulfill a promise to help a orphaned relative after it became apparent that she spends the money on unnecessary luxuries?

We advise you to continue assisting the orphan, directing the expenditure towards important matters and avoiding extravagance, or by providing her with her in-kind needs.

If you wish to stop the expenditure, the phrase "I covenant with Allah" is considered an oath by the Hanafis and Hanbalis, and it is obligatory to fulfill it. If you do not fulfill it, then you must perform an expiation for breaking an oath (feeding ten poor persons, or clothing them, or freeing a slave, or fasting three days if you cannot find these). This applies if it was an explicit statement and not merely an intention.

As for your promise to her: If you intended to fulfill it, then later decided not to for a valid reason, there is no sin upon you.