Unpopular opinion: nobody reads the second player's screen in split screen games and it ruins everything
I was playing It Takes Two with my buddy Dan at his place in Cleveland last month and we got stuck on the same boss for 45 minutes because he kept watching MY screen instead of his own. I finally paused it and asked him what color his half of the arena was and he had no clue, he was literally playing blind the whole time. This happens with like 8 out of 10 people I play split screen with and I think it's because solo gaming trained everyone to stare at the center of the screen. In a real co-op game your half is your half, you have to trust your partner to cover their side or you both die. If you find yourself leaning toward your friend's half of the TV, that's your problem right there. How do you break this habit with someone who swears they were watching their own screen the whole time?
The bigger issue is that most modern TVs have terrible viewing angles for split screen. If you sit even a little off center, the other half of the screen literally looks brighter or washed out, so your eyes get pulled toward your partner's side without you even knowing. Dan probably was watching his half, but his brain kept drifting to the crisper looking side. Try having him sit closer to the TV or directly in front of his half, and see if the problem fixes itself.