Don't know about the 09-10's, or what year your Vibe is, but if its a 03-08, one thing to try is to disconnect the electrical connector from the inverter under the driver seat, and then see if the fuse still blows when you press the switch. If the fuse still blows, then it is likely the wiring or relay supplying power to the inverter, if it doesn't, then its likely the inverter.
The inverter has overload protection built in, I know when I have tried to power something that needs more power than the inverter can supply, it just shuts down until the overload is removed, then it recovers automatically, doesn't blow a fuse, so if you have a wiring short on the 115V AC side, it won't blow the fuse.
If you think that inverter is bad, then maybe you could reach out to bratboy, in
https://forums.genvibe.com/phpBB3/viewt ... 18&t=47702 he said he has about 5 of them
and since this looks like your first post, welcome to genvibe!