Here, 'should have', as a modal verb, is correct because should is used after 'that' when something is suggested. Here, it is ...suggested that she have a party...
'Will' is used for talking about or predicting the future. Example: She will go for a movie tonight. 
'Has' is used when the subject is a singular noun or singular pronoun. Example: She has, he has etc. 
'Will have to' is incorrect because it does not fit in the sentence.