Do a couple of easy checks before you start throwing money at it. Measure your battery voltage at the starting battery with everything turned off. Hopefully it is at least 12.4 volts (should be 12.6 or greater). Then start the engine and remeasure volts at the battery. Should be well above 13.6 and likely 14.5 or so. If this measurement works then turn on everything you can think of. Remeaasure voltage both starting and house battery. The alternator should keep voltage roughly the same as the original running voltage. If the alternator doesn't put out close to 14 volts with minimal load and maintain that voltage with everything on then your alternator is not working correctly or not large enough. 63 amp seems low so if you do replace I would get at least a 90 amp if not larger, and no there is no such thing as too large within reason.
