Burns,
The alternator problem can be solved. Radio Shack has a filter for this, about $15 or so.
The inverter noise is another problem. I'll assume that the inverter is a modified sine wave one. If it is the only economical solution is to turn off the charger while listening to the sound system. The problem is that the manufacturer did not provide for interference suppression and to add it now is very expensive and is not likely to work. If you have a Xantrex, the filters for the AC lines are over $100 each. The DC filters are even more expensive. In addition to all that you have to put the whole inverter in to a metal box with the filters at the connections to this new box.
Bottom line is after all this, you may still have interference.
The only real alternative is to change to a sine wave inverter and hope the charger is well designed.
I have a similar problem and just turn off the charger and hope for the best. When I am using my SSB Ham radios, I turn off both the inverter and charger and run from the batteries unless SWMBO decrees that she will use an AC device. Then I get along as best I can.
