Okeydokey Pokey. There is an easy button for shore power here.
First question - are you using the solar panel input on the Renogy DC-DC charger?
If no - connect a 24V, 10A "outdoor lighting transformer" to the solar input on the Renogy.
Set the Renogy max amps at 10A - you need the remote screen for the DC-DC which is a separate part. Set it back to 50A when charging off solar or the alternator.
Plug in the outdoor lighting transformer - boom shore power that will also float your starting battery after your house battery is charged.
If you ARE using the solar input on the Renogy DC-DC (you have solar panels?), do the exact same thing, but use a relay to cut the solar panel feed when using the outdoor lighting transformer. This relay can be powered by the outdoor lighting transformer.
The theory of operation behind this is you want to charge both batteries - house and starter. You want to be able to plug in, but you don't have huge A/C draw when plugged in - no hot plate, no A/C, no microwave (assuming). You just need to keep your house battery topped up when plugged in. Use the house battery to absorb the high current surges and use the low current transformer to keep it topped up.
The reason to use the 24VDC outdoor lighting transformer on a 12V system is twofold - firstly the Renogy DC-DC won't charge from the solar input unless it sees over ?17? volts (going off memory) and since 24V 10A is the same as 12V 20A (but wire gauge is half since voltage is doubled (ok not really drop the pitchforks but thats the gist of it)) its a lot easier to wire it in. Same amount of wattage, easier wiring, cheaper transformer.
The reason to use the solar input on the Renogy vs any other input or connection point is that is the only point in your system where you can apply power and charge house and starter batteries from a single charger.