I can't really tell what that is a photo of. The starter relay/starter circuit should not have anything to do with the charging circuit.
The starter circuit should have a heavy wire from the battery to the 5/16" stud on the starter relay. A wire runs down to the starter solenoid from the relay. There is also the heavy red cable from the battery. On the starter relay there is a wire from the ignition switch to turn on the relay in the crank position of the ignition switch and if its an automatic transmission car a wire from the neutral start safety switch. Both of these wires energize the starter coil and this should only happen if the car is in park or neutral.
The charging circuit is: The heavy black wire from the alternator output stud, to a bulk head connector pin, to a connection of wires Chrysler calls a "splice joint" a black wire runs from this splice to one side of the ammeter. The other side of the ammeter has a red wire the runs back out through another bulk head connector pin to the fusible link. The other end of the link goes to the 5/16" battery stud on the starter relay and on to the positive side of the battery. This battery stud connection point on the starter relay is the only point the starting circuit and charging circuit come together and it is only used as a tie point. One circuit really should not have any thing to do with the other.
The more you tell us about the wiring in this car, the more I think its really been hacked up and it may be time to think about some new wiring harnesses to put it back the way it left the factory if the car is ever to be reliable. Especially if its going to be driven daily by your daughter.