I like to think about charging a battery like this. You are trying to pump water up to a certain level through a very small pipe. some of the pressure is used up just to make the water raise up to the level of the spot you are trying to pump it. The rest of the pressure is used up overcoming the resistance of the small pipe. Now if you add a pump and another pipe, and the pressure is exactly the same, you will pump twice as much water. But if the pressure is off just a little bit, the flow will differ considerably between the two pumps, because most of the pressure was used up in overcoming the head pressure, and it's only the difference between the head pressure and the pressure of the pump that drives the water..
Say a battery is at 12.5 volts, and your charger puts out 13. The resistance of the battery is a half an ohm, and the resistance of the charger is a half an ohm. You use up 12.5 volts just to get the electrons flowing. All you have left is a half a volt to push the current through the one ohm of resistance. So you get half an amp of current, and now the battery has 12.75 volts on the terminal because of the voltage across the internal battery resistance. Now say you have a second charger you want to add. It only puts out 12.75 volts. Everything else being the same, absolutely no current will flow through your second charger. Because it can't overcome the head pressure (voltage) of the battery! And only because of a quarter volt difference.
So the chargers really aren't fighting each other, you might just find that if you buy 2 ten amp chargers, one might be putting out 8 amps, but the other only puts out 2. Especially if one of them is the trickle charger you mentioned. It charges at a slower rate because it puts out less voltage, and has a higher internal resistance. If you want to parallel chargers, they should be the same rating.
I experienced this back in the day working on old twin engine airplanes. They both had big dc generators (one per engine) that were paralleled together. Periodically you had to run both engines and precisely adjust the voltage regulators so that each generator put out the same current. Didn't take much adjustment to make a difference. later I started working on Boeing 727s. They had AC generators that were paralleled. But it was much more complicated. The airplane automatically adjusted the voltage regulators to equally share the reactive power delivered by the generators, and it drove the drive units for each generator harder or easier (speed control) to equally share the real power. But that's another story. Suffice it to say that DC stuff isn't too hard to parallel compared to AC, but a little change in voltage goes a long way.
Back to your battery. I say go to goodwill, a flea market, estate sale, or elsewhere and pick yourself up a good used battery charger. Probably cost about 5 bucks. I'd be nervous leaving an expensive car like the leaf sitting around for a long time with the system on, and jumper cables connected to the battery.
