Online/ split screen will be a huge improvement to the fallout series. You will have to make it harder difficulty and have to make players stay in the same radius. When a player tries to fast travel the other player will have to Accept/ Decline.. same thing for entering buildings. In the game kill stealing might also be involved alot. What you should do is, the player who killed the enemy gets full points and the second player gets half points. When players talk to NPC's the other player will stop and have to wait for the conversation to end (to avoid quest glitches etc)
Now alot of glitches might result as this, but patches will help and if players are too disappointed they can just play single player as it was meant to be.
Please fellow friends and fans of Bethesda, support this topic and add suggestions of what you think might make online better or more successful and/ or what they should do.