Washing hair is necessary in ghusl since ghusl by definition is washing of the whole body, which includes the hair. If washing hair regularly causes it to be weak then you should consult a dermatologist as there might be solutions like using a moisturizer or taking nutritional supplements. You can also consider alternate means of intimacy where she does not need to perform ghusl (intercourse in other than the vagina).
It is obligatory on a wife to obey her husband, especially in matters of intimacy. She can not legally refuse without a valid excuse such as a situation which makes it haram for her to have intimacy. Inconvenience is not a valid excuse.
And this is apparent from the following ahadith:
لو كنت آمرا أحدا أن يسجد لغير الله لأمرت المرأة أن تسجد لزوجها والذي نفس محمد بيده لا تؤدي المرأة حق ربها حتى تؤدي حق زوجها ولو سألها نفسها وهي على قتب لم تمنعه
If I were to command anyone to prostrate to anyone other than Allah, I would have commanded women to prostrate to their husbands. By the One in Whose Hand is the soul of Muhammad! No woman can fulfill her duty towards Allah until she fulfills her duty towards her husband. If he asks her (for intimacy) even if she is on her camel saddle, she should not refuse.
— Ibn Majah , Abu Dawud
إذا الرجل دعا زوجته لحاجته فلتأته وإن كانت على التنور
When a man calls his wife to fulfill his need, then let her come, even if she is at the oven
— Jami at-Tirmidhi
لا تصوم المرأة وبعلها شاهد إلا بإذنه
A woman should not fast (optional fasts) except with her husband's permission if he is at home
— Bukhari - because fasting prevents intimacy
إذا دعا الرجل امرأته إلى فراشه فأبت أن تجيء لعنتها الملائكة حتى تصبح
If a man Invites his wife to sleep with him and she refuses to come to him, then the angels send their curses on her till morning
— Bukhari
والذي نفسي بيده ما من رجل يدعو امرأته إلى فراشها فتأبى عليه إلا كان الذي في السماء ساخطا عليها حتى يرضى عنها
By Him in Whose Hand is my life, when a man calls his wife to his bed, and she does not respond, the One Who is in the heaven is displeased with her until he (her husband) is pleased with her.
— Muslim
Also see https://islamqa.org/shafii/seekersguidance-shafii/168834/my-husband-wants-marital-relations-every-day-and-washing-my-hair-so-often-makes-it-fall-out-what-do-i-do/ and https://islamqa.info/en/answers/2648/