This was sweet. Let me point out some things to make this a better read though, okay?
One - Your second sentence has a mistake. "..one of the few woman (women) I could smile at"
Two - „I'll come by later", ("words," he/she said - is the right format - example: "I believe you," Carlisle whispered /OR/ Carlisle whispered, "I believe you.") In the beginning you used ,,this" and then later changed to "this"
Three - "30 seconds later" (use the word "thirty" - it isn't a big number, try to make it a point that you only use numbers in stories when for example, you're mentioning a year, like 2012.)
And four - remove this (LEMON very graphic sex-secene) from your summary. There isn't one at all.
Other than those, the story was utterly sweet, I liked it. :) By the way, I was just helping out, if ever you thought of editing this piece to make it look perfect. I hope you don't mind and I hope you didn't take it the wrong way.
-Aoi.

A very touching moment between Carlisle and Esme.

This was really good. CarlislexEsme all the way, baby!