By your statement it looks like current leakage in the wiring. First of all get a load test of your generator by battery shop with and without load. If it shows good charging, then further proceed to the ignition switch part, as it might have problematic contacts that worsens upon heating (you can feel by the hotness of key after some time of usage). If it still doesn't resolve the issue, get complete wiring replaced. I recommend that before changing the wiring, at-least get the ECM scanned for general parameters read out and error codes. BTW the battery wire burning during alternator installation can be due to mis-handling too!