What is the subject of the relative pronoun of that?

'Featuring floral patterns, religious symbols, and messages of hope, the painted henna crowns are amazing substitutes for the hats and wigs that the cancer patients would otherwise use to cover their heads.'

1.What is the subject of the relative pronoun of 'that'? 'Substitutes' or 'the hats and wigs' ?

2.What does 'otherwise' mean here?

Thank you for the help.

First, the thing that a pronoun represents is not its subject but its antecedent.

Second, the antecedent of that in this sentence is hats and wigs.

Third, otherwise means (more or less) in other circumstances. The patients are not wearing hats and wigs for some reason or another, so those hats and wigs are described as the hats and wigs they would be wearing if that reason did not exist. (However, the reason does exist, so the patients have substituted painted henna crowns for the hats and wigs.)