"So long as our relationship is defined by differences, we will empower those who sow hatred rather than peace, and who promote conflict rather than the cooperation that can help all of our people achieve justice and prosperity. This cycle of suspicion and discord must end."

"So long as our relationship is defined by differences,
So long as 是“只要、如果、假如”，表示假设。
defined 是形容词，表示“定义明确的”
our relationship is defined 就是“我们之间的关系定义非常明确”
by 就是“通过……”

we will empower those who sow hatred rather than peace, and who promote conflict rather than the cooperation that can help all of our people achieve justice and prosperity.
empower 是“授权”的意思。也可以理解为“放纵”
those 指代who后面形容的那种人
rather than 是“……而不……”的意思
that后面的从句时修饰“the cooperation ”的，表示这种合作能够帮助我们所有人实现公正和繁荣。

This cycle of suspicion and discord must end."
cycle of 可以是“……的循环”，也可以是“一系列……”
suspicion and discord 是一个整体，都是跟在“This cycle of ”后面的。

“假如我们之间的关系通过分歧而变得明确，我们就会放纵那些散布仇恨而不是传播和平的人，还有那些发起斗争而不是促进合作的人，而这种合作能够帮助我们所有人实现公正和繁荣。这一系列猜疑和纷争必须被终止。”