There is a second case, which would likely through everyone on the Kiwi Forums a MASSIVE curveball, but I think this should be seriously considered:
The assumption that Cole and Chris split Barb's belongings upon her death in the absence of a will only holds if they are the only children of Barb. This is not an assumption I think we shouldn't automatically consider as true. Chris was the product of the final man in Barb's life. Cole Smithey, the child of one man and the alleged (by Barb) son of a second man.
Barb, even in her 20s, is still not going to be a great partner. She's dishonest, ruined her family ties by trying to seduce her in-law, and per Chris, claims to be unchaste even in high school. People at this age don't fully understand one of the great rules of dating--never stick your dick in crazy. In the late 50s, Abortion was illegal, the Pill had yet to become common, and she didn't allegedly marry Ran Coleman Yeatts until 1961. This is a gap of something like five years or so.
A Third Child of Barb, perhaps given to a relative or otherwise hushed given the shame it would cause, doesn't lose inheritance rights just because they're born out of wedlock. If such a child was born, they would have a one third stake in Barb's estate. And this child would have been cut off from Barb, carefully concealed (much like Cole's Parentage) and may very well feel entitled to something from a mother that never did anything for them while alive.
This is just speculation, but this is definitely possible.