take care of myself in the better way that you ask.帮我看看这句话这样

你给的几乎就正确了,只要稍微改动就行了：
Take care of myself in the better way (that可省略) you 【asked me to（承前省略了take care of myself）】.
或者：
Take care of myself in the better way (that) you 【wish/expect me to】
注意,用hope,可表达为：
Take care of myself in the better way (that) you hope.
因为,【hope sb to do sth】,这一结构是【错误】的!
其实,很久不用,你能写出这样的句子应该很不错的,只要有空再坚持学一点,你又会很出色的!
祝你开心如意!O(∩_∩)O~~