SC power supply charging?

Usually a converter is wired directly to the battery (via fuses / circuit breakers as needed to protect against short circuits). Converters are designed to not overcharge the battery even if connected and powered for a long time. The converter is also probably capable of putting out a lot more than 15A DC: typically it would be rated around 40A to 60A or so. That rating is a maximum current; it's basically a voltage regulated supply and so will only supply as much current as is needed to maintain whatever output voltage it's set to. If it's a multistage converter--which I would not really expect--the output voltage setting will vary depending on what mode it's in, higher for the initial charging of a depleted or partly discharged battery and the lower to maintain a full charge.

The solenoid is likely not directly related to the converter. It may be a battery disconnect solenoid, which is a single pole latching solenoid: apply 12V momentarily in one polarity to the control terminals to turn it on, and in the reverse polarity momentarily to turn it off. The control wires would generally go to a center-off DPDT momentary switch. It may also be a battery combiner relay that connected the house and chassis 12V systems of the motorhome together when the engine was running (to allow the alternator to charge the house batteries while driving), in which case it would be a continuous-duty single pole non-latching solenoid.