Maya,
I wouldn't get a new deep-cycle until you need it. If you do you are going to have to maintain it also, and the warranty may run out before you even use it.
Spend your money on the charger.
Even old RVs typically have an automatic connection to the house battery when the ignition is on. So, your house battery does get charged when you are travelling. The way to test this is start the engine and then measure the house battery voltage again. It should be 14v plus. If it still reads 12.4 then either you don't have the device or it is not working.
>Ok so basically I should have a wire running from the the terminal marked battery on that black fuse box I took pic of to my house battery ?
Yes, you can try measuring contiuity across it and the positive side of the house battery. To be sure you should disconnect it at the fuse.
