Cancerians will put family first and her family is going through a lot of crisis right now. She will not up and leave them at this time. Even when her father heals, it will not be easy for her to move away from family.
The hard truth for you to face is that she will put her own wants and desires below what is in the best interest of her chidren. Their father will be a part of her life for that reason.
I'm afraid that she is putting off the move because of her complicated family life. She could feel torn between a life with you and her present living situation.
Now is not a good time to force a decision. Let her grieve for her aunt, care for her father and raise her children (with the help of her ex). Just be supportive and loving and willing to do whatever it takes to be her partner.
Consider moving to her town. Or nearby, at least. Would she like that? You could sell or rent your house.