You cannot get through to him. He is the only one that can change his perspective. You could get through to you though. See things for exactly what they are and not for what they should be or what you would like them to be.
Dwelling on the "shoulds" is the road to hell. Whether he should do something or not is irrelevant. He isn't doing it. Get really clear with what is and then make some choices and decisions accordingly.
If you release all of your shoulds about him and simply accept what is you are then free to care for yourself and your daughter in the healthiest way. For example, if he doesn't help with housework and you need help, hire some help or re-prioritize or let some things go (like all of his stuff).
Create clear boundaries for yourself and then follow through. Find a really good counselor to support you in seeing what is and then being able to have the hard conversations and make the hard decisions. It is likely with what you have shared that he will be resistant to any counseling. Focus on you. Get support for yourself.
As you heal, he will be left with some choices of his own. The kindest thing you can do for yourself, your daughter, and him is to allow him to be who he is. At the same time, shift focus to you. You have things to heal and learn about yourself that have contributed to you choosing this man and to you tolerating his behavior. There are things that keep you from setting boundaries and standing up for and caring for yourself. Heal these things and you will be amazed at how the world around you changes.
"When you change the way you look at things, the things you look at change."
A couple of really good resources that might help are:
The Work by Byron Katie, www.thework.com -- she has some amazing tools to support you in questioning your thoughts and being able to move past all of the shoulds to a place of choice. Many of her videos are free, there are a ton of youtube videos of her doing the work, and all of her worksheets are free.
"Boundaries: Where you end and I begin" by Anne Katherine
"The Art of Extreme Self-Care" by Cheryl Richardson