FYI... any battery that is labeled with "CCA" (cold cranking amps) is made to be a "starting" battery and is not designed for multiple drainage. It provides large amount of amperage for a short period of time to start engines with. It will NOT provide that same amount of amperage over a longer period of time.
What you need is a "Deep Cycle" battery that is measured in "Ah" (Amp-hours). Look for one that is at least 100 ah. Yes, you can connect the tv's battery via cables and yes you can connect multiple 12v batteries in parallel.
Keeping the rv plugged into your house may or may not keep the batteries charged. It all depends on the type of converter/inverter you have. It needs to be a three stage that provides a "float" charge to keep the batteries at maximum charge without boiling them over.
Hope this helps
Ron