having been told three times,she was so angry that ...

这句话并不是主从句或者谓语动词时态的问题,因为前面那个部分having been told three times不是一个句子,它只是后面句子的一个修饰成分(状语),所以不能用have的原型,而是要用动词的非谓语形式.
而having done 和having been done是非谓语动词里面两个结构,一般做状语,表示这个动作(done)发生在后面句子中的谓语动词之前.
这句话是想说她被告知了三次之后她就生气了,“被告知”是发生在“生气”之前的,所以用having done 或having been done这种形式.
而having done 和having been done的区别就是having done 是主动having been done是被动.
这句话里面主语是she,she和前面的动词told来看是她被告知,所以是被动,所以用having been done,所以说having been told