这句话对吗Having back on that performance,she realized that she had never felt so alive.

二楼说的基本对，但是要纠正两个地方。
第一，这里不能用gone,而是要用been！have gone的意思是已经去了，可能在路上也可能是到那个地方了，而have been是去过那个地方。这句话是说她回来了，所以是去过那个performance，所以这个地方要用been.
第二，Having back on that performance 并不是动名词作时间状语，而是动词现在分词作状语。虽然动名词和现在分词表面上看起来都是doing形式，但是还是不一样的。动名词是名词，名词是不能做状语的～
另外我觉得这个地方的on也挺别扭的，要是我说我会用from
所以我觉得这句话应该写成：Having BEEN back FROM that performance,she realized that she had never felt so alive.
或者Back FROM that performance,she realized that she had never felt so alive.

Having (gone) back on that performance,she realized that she had never felt so alive.

这里的主句是 SHE REALIZED THAT SHE HAD NEVER FELT SO ALIVE,是一般过去式,宾语从句里用的是过去完成时.Having back on that performance 是一个动名词短语作时间壮语,所以必须添加一个过去分词 GONE,才能表示这是早已发生的事情.正确的写法是：
Having GONE back on that performance,she realized that she had never felt so alive.
也可以改写成
AFTER (WHEN) SHE HAD GONE back on that performance,she realized that she had never felt so alive.

Go back to that performance,she realized that she had never felt so alive.