After James has injured Bella and she is in the hospital, Edward is trying to reassure Bella that he will stay with her. He wants her to rest and heal.  She wants assurances that he will not leave her.  Part of the reason you are having difficulty with Bella's responses is that you are ignoring the last part of Edward's statement.  Edward says:

"'I will,' he promised. His voice was beautiful, like lullaby. 'Like I said, as long as it makes you happy... as long as it's what's best for you.'"

"I tried to shake my head, but it was too heavy. "'S not the same thing,' I mumbled"

The part of the statement that Bella is responding to is that section which reads, "as long as it's what's best for you."  There is a big difference in telling someone you will stay with them as long as it makes them happy and saying as long as it is what is best for them.  Someone may feel that they are happy with a person when it is not necessarily what is good for them.  Edward is saying as long as Bella is safe he will stay.  Bella wants an unconditonal commitment.