Of course, if the gerund after "dislike" begins with "having," you can follow "having" with "to wait":
I dislike having to wait. (= I don't like to have to wait.)
It isn't. Without "to have", you dislike the wait; with it, you dislike the necessity of waiting.In my opinion saying 'to have' in the sentence 'I don't like to have to wait' is redundant.
To leave it out would remove the idea of obligation. I don't like to wait and I don't like to have to wait have different meanings.
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