My italian greyhound is age 6. She continues to eliminate on the rug in the nighttime (mostly just pooping, but sometimes pees on the rug) even though we have a dog door, potty pads, and it is warm outside. What can I do to prevent this? Should I have her sleeping in a kennel?

Has she always done this or is it a recent development? Any change in food, change in lifestyle (new pet, new baby, just moved)?

I think I would do the crate at night, and then go out with her in the morning and praise, praise, praise when she poops out there. Also if you catch her pooping in the floor, yell no or shake a can of pennies to startle her into stopping, run outside with her, and praise like crazy when she finishes OUTSIDE. Basically, I'd go back to square one as if you are training a puppy.

Get used to it, IG's are not known for good potty habits. They are creatures of extreme comfort even if that means not going out in the dark to potty. Most breeders or rescue's will make sure that the occasional accident is alright the people acquiring one because it's almost a given. Crating at night may eliminate the chance but I know how bad their anxiety can be.