Note, unless:
1) an smtp server is actually listening at the domain (have you tested this?);
2) is configured to receive any address at the domain;
Then your confirmation emails from yahoo are getting refused by the other domain. So there is no guarantee the other domain has, or does not have, your reset emails. In any case, unless you want to try to buy that other domain just to get your own reset emails, you'll need to contact yahoo support, they are the only ones who can help you now.[edit: formatting]