这句话中有点不理解,帮个忙I wanted to let you know that james and I will

这里的 go stay = go and stay ,是一种缩写
我想让你知道James 和我明天将离开这里去我姐家里逗留一会.
for a while 暂时 一会儿 一时

I wanted to let you know that james and I will leave here tomorrow to go stay at my sister's for a while.
leave应该是原型吧
james and I will leave here tomorrow to go 可也看作是一句话
james and I will stay at my sister's for a while. 可以看作一句话，也就是说主语都是james and I

go stay at是一个词组，意识是去呆在某地。英语中这样的语法是很常见的。

means go and stay at my sister's home.是一种缩写吧。
如玩狗时，Go get it .让狗取东西