Hmmm. I would troubleshoot your electrical issues before you look at the weak spark issue.
If your generator and your battery are good, but it keeps dying after you charge the battery, chances are you have a drain. Disconnect and charge the battery, hook up the ground and hook up an ammeter inline with the positive. Key off you should see very little current (not sure what exact spec is, but definitely shouldn't be more than 1 amp, a few mA is all thats allowed on cars). If that checks out, you may have a short to ground when the key is on.