She MUST go is correct ! went is past tense, not to be used here. She went home and said to her husband that the doctor (told her / asked her) to go on a holiday to the seaside ...

Must is a modal verb, so only a verb in infinitive form can follow it. Interestingly ''must'' IS a past form... the present form is completely obselete. To answer your question, to express ''must'' as a past obligation, use ''had to''. You'll find this in any English textbook. ''She told her husband that the doctor said that she had to go on a holiday...'' (I cleaned up the rest of your sentence as well.)