INCORRECT USE OF PREPOSITION

Here's my stream of thought on this one. 

I would probably change it a bit differently because I'm not fond of repetition in the same sentence.  You are saying that there is no greater feeling than than to know this, that & the other thing.  Rather than adding a second to know that, I would think to write it more like a list of the three things to know. 

However, it gets a little more confusing because "you are loved and cared for" is really one item on the list, not two.  To make it two separate items, we would have to say you are loved and you are cared for.  So, that leaves us with either saying you are twice, or to know that twice. 

Since neither of those options are particularly appealing to me, I believe a third option is to make it into two sentences.  Doing so adds some emphasis (in my opinion) on what becomes the second sentence by giving more description on what that great feeling is. 

There is no greater feeling in this world than to know you are loved and cared for.  It is comforting (reassuring/a relief/encouraging) to know that when things go wrong -- love will carry you through.