connect coach and house batteries?

It sounds like you may want to find out what is drawing on your chassis battery that's causing it to drain like that before going through any mods. A chassis battery should not discharge completely in a week. Something is drawing it down - a light left on, the radio etc. You could (or should) install a disconnect on the chassis battery and shut it down prior to putting the RV away for any length of time. Granted an alternator could be part of the problem but it sounds like it's going dead in a week of sitting and not running in which case neither is the alternator.

You did mention you just replaced the batteries. Did this problem occur before you replaced them?

If you wanted to try to see if a solar charger would help, try a stand alone model for little cost before running any wires.

Car solar charger