Way back when, Chris contacted Cole from out of the blue to ask him to vote for him in the Parappa sweepstakes and, when Cole agreed to vote for him in exchange for Chris finding out who Cole's real father was, Chris did a half-ass job of it.
When Cole got married, Chris made some kind of video where he said "Whoop-dee-doo for you" and implied that Cole should be taking care of his mother.
Later, Chris informed Cole (via social media) that he needed to move back to Virginia to take care of Barb in her declining years and, when he got no response, Chris drew a picture of Cole living in Carnegie Hall and burning stacks of dollar bills.
Chris has also made a voodoo doll/Lego figure of Cole and pitted it against Chris-Chan Sonichu or Collossal Chan or some such shit.
While there may not be hostility between the half-brothers, it's safe to say there is no love there.