For the problem with the 2nd player score reels not resetting, you'll want to find a circuit that includes a score motor switch, which is related to all the 2nd player score reels. Score motor switch 1A with the orange/blue wire is related to all the 2nd player score reels. Make sure score motor switch 1A is clean and adjusted properly.

For the second problem with the machine switching between players, there is an alternating switch that makes each one of the players active. Part of the schematic you posted is cut off, so I can't see that switch. Looking at other Gottlieb schematics, it would be a switch like P2B. On the schematic, look for switch "L" to the right of the add 2nd ten thousands unit solenoid, and follow the circuit until it gets to a switch similar to P2B. Make sure that switch is clean and adjusted properly...

Be sure to clean the suspect switch contacts with a Flexstone or paper fingernail file. Sometimes you have to "scrub" the contacts to get them totally clean. Also, make sure all the switch stack screws are tight...

As HowardR said, it's best to work on one problem at a time, so let's continue to troubleshoot the 2nd player score reels and why they aren't resetting completely at the start of the game.

Some simple checks: Check the Jones plugs in the backbox to make sure they are clean and tightly seated. And, with the power off, manually rotate the score motor disc and observe how all the switches and switch blades open and close. Look for anything "strange" going on with the rotation of the score motor.

Going back to the question - what do the 2nd player score reels have in common with a circuit that the 1st player score reels don't have in common? Back to the player unit, switches P4A, P4B, P4C and P4D are only related to the 2nd player score reels. Check those switches - clean the switches; check if the switch stack screws are tight; check for shorting wires at the switch stack lugs; check for missing switch contacts; check for switch blade alignment. You can manually advance the player unit with the power off to see how the switches operate...