Should I fight for my relationship

I want to start by saying thank you for letting me know about your situation and trusting me to answer your question. However as you may already have presumed, I can't make this difficult decision for you. This is a serious thing to contemplate, and I hope I can reflect and ask the right questions so ultimately you will feel empowered to make the decision you feel is right! With that said, here are some of my thoughts:

I personally believe in looking at the facts. From what I am hearing, it sounds like his actions are not supporting you in the relationship. While there is definitely an emotional connection, try your best to set that aside and ask yourself if he were to never change would you be okay/happy/satisfied in this relationship? If so, for how long 5/10/20 years?

I believe we should marry people based on who they are, not on what they could become. That doesn't mean you shouldn't give him a chance, but it sounds like you've made your concerns known and he isn't making any effort to assure you he truly is who you need him to be. However, I also only know a small part of your perspective. So I urge you to think about all the reasons/facts he IS who you want and need. Try to think of this as logically as you can.

No matter what decision you make, it sounds like the decision will be very hard. If you stay, you will possibly have many moments of feeling unloved and having to work through that and hope he can do better. If you leave, you are leaving behind someone you really love and his family that you love as well. At the end of the day though, you will make the decision that you know is right and will need to trust that the hurt and pain won't last forever. 

I also encourage you to speak to someone who knows you and him and your relationship. They may be able to shed some light on the situation and offer you a different, or more accurate, perspective!