I promised myself that if he went back to her again without trying things with me properly then I would definitely call it quits as I am tired of being in this madness. But now I don't feel so sure. If I let him move in, maybe he would make more effort? Who knows.
Who knows? YOU DO.
Dayana, DO this (give in to his childish, petulant emotional blackmail demands), and you'll be destined to a life of "more of the same" from him, including other woman (or even women -- plural) for the rest of your life.
You were given great advice above from Coach and PMABaby. I'd suggest you follow it, and STICK TO YOUR GUNS. Is this (giving in to a man's crap behavior, so long as he badgers you enough) what you want to teach your daughter? Please consider this, and then re-read it slowly: She is about to head into her formative years for how she will relate physically and emotionally to the opposite sex for the rest of her life.