to be patient with someone until he/she is willing to ...
ーI will wait until my son is ready to go to school.
「息子ご学校に行くまで待ちます」
to wait until someone is ready to ... で「人が…する覚悟・準備ができるまで待つ」
ーI will be patient with my son until he is willing to go back to school.
「息子がまた学校に行きたがるまで待ちます」
to be patient with someone until he/she is willing to ... で「人が…したがるまで辛抱強くいる」
ご参考まで!