ように～てほしい

ように～てほしい says what you want someone else to do and what for: "I want you to do B so that A". The goal comes first, in the dictionary form or the ない-form with ように; the action you want follows in the て-form with ほしい.

The goal clause takes a verb nobody does on purpose: a potential verb, an intransitive verb, a negative. The person you want to act takes に.

てほしい or たい

たい is only for what you yourself want to do. For what you want someone else to do, use てほしい.

• × 遅刻しないように早く起きたい (for "I want you to") → 遅刻しないように早く起きてほしい

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ほしい states your wish directly, so it suits family, friends and people below you. Add んですが to soften it, and to someone above you ask with ていただけませんか instead.