G6 standard bolt pattern is 5x110mm.
Providing the rims are the same size (say 16"), and how much more the rims are worn (from removing/installing), it might have been a fluke that the 5x114 rims fit on the G6. a 4mm difference isn't all that much, but it does make a difference as you've found out.
The only way to make them fit is getting a custom hub, or adding a spacer which I can't say I'd recommend for the G6, as the wheels would have to have a big offset to countermand the spacer or else once you install tires, they'll rub and possibly cause a whole load of problems.
Frankly, it's not worth while to squeeze on rims that aren't the right size. You were lucky that the other rims fit, but if they have a different diameter, it might be more of a brake caliper clearance issue than anything else. I'm no wheel expert by any means, but I'd stick with the proper size.
Providing the rims are the same size (say 16"), and how much more the rims are worn (from removing/installing), it might have been a fluke that the 5x114 rims fit on the G6. a 4mm difference isn't all that much, but it does make a difference as you've found out.
The only way to make them fit is getting a custom hub, or adding a spacer which I can't say I'd recommend for the G6, as the wheels would have to have a big offset to countermand the spacer or else once you install tires, they'll rub and possibly cause a whole load of problems.
Frankly, it's not worth while to squeeze on rims that aren't the right size. You were lucky that the other rims fit, but if they have a different diameter, it might be more of a brake caliper clearance issue than anything else. I'm no wheel expert by any means, but I'd stick with the proper size.