The double sider you speak of is known as a 'dual chipper'. It's a club designed for chipping using a putting stroke, rather than using chipping form with a wedge (or iron).

I'm not aware of any rule regarding the handedness of the clubs in your bag. If you want to carry a left-handed club, it's probably ok. (and not a bad idea if you're just looking to take a stroke to improve your lie).