Your above sentence has two clauses/senteces. One is the main clause and the other is reported clause.when reporting what someone else has said, the reporting verb in the main clause is usually in the past tense. The rest of the sentence is normally past too, and the reporting clause is introduced by a linking conjunction such as that or if which follows the reporting verb: So here the verb in reported clause should normally be in the past tense as:
I told her that she would need (needs) to send her dad an invitation.
I told her that she should send her dad an invitation. (better)
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