No, having multiple charging sources all charging at the same time will not hurt at all. The lesser voltage charge will not even matter, it is only the highest voltage charger that is charging assuming the battery is not near depleted. IF depleted then the others might contribute, but that is info that is really of no use to discuss.
You are in TC forum so possibly your batts are closer to the alternator than would be in a trailer, but unlikely as I always see the wires connect from the back of the truck, then run in the bed to the front of the TC then out to battery. If you want more from your alternator then shorten that distance, cut out the going to the rear of the truck, and just wire up through the front of the bed and somehow run the wire as direct to the battery as you can.
Anderson plugs are good for making the connection.
Otherwise the slow charge from the way it is will be fine.
You can run solar, be plugged in with your charger going and run the truck motor/alternator and this is fine for the battery.
The best charging is an AGM specific "smart" charger though.