The only way there are survivorship rights in NC is if the deed specifically says they are there. Just joint isn't sufficient. Tenancy by the entirety would be sufficient, but since D and P aren't married, that's not an option.
Secondly, I think an explanation is owed as to why this glaring, but wholly irrelevant contradiction in your clumsy narrative:Lastly, unless D and DF took title to the home not as tenants in common, but as joint tenants with rights of survivorship (j/t/r/s) then DF better come up with something more substantial than(1) D never lives in the home, yet (2) D's child P does not like DF is living with D [sic].Otherwise DF could very well be facing an indefensible Petition to Partition the property. Which if pursued to fruition could result in the property being sold at a public auction with the only bidders being vultures looking to steal it.D states that once D is dead, home will solely be DF's.
I don't know where you fit in here, but if your loyalties are with DF, you would do well to have her consult with her lawyer.