Halo 2/2A Split-Screen Online Jitter+Drops Frames

I recently was able to play split screen online on my Xbox One S with my friends locally. 3 Player Split screen worked perfectly, with no frames being dropped or any choppiness when we played Halo CE maps or Halo 3 maps in matchmaking. However, when playing either Halo 2 or Halo 2 Anniversary, there was significant choppiness and lag. The game was jittery, and it made it really hard to play a matchmaking game because of the lag.