Cat Pooped on Bed!!!!

2 litterboxes, one where the dog has no access to the cat.
The dog might be chasing the cat away from the litterbox and the cat is now afraid to use it. Or the cat is simply holding it in fear of the dog and when she finally had to poop she pooped wherever she was. And it could end up setting a pattern for her. But she is obviously terrified of the dog and that most likely won't change. Not with the mentality of a Siamese cat
or if worse comes to worse [linkhttp://www.siameserescue.org]http://www.siameserescue.org[/link] we get siamese all the time that simply cannot coexist with other pets.
They might get along fine with another cat their own age but not dogs, or dogs but not cats. I had a foster this summer that was great w/my dog and now lives with 2 greyhounds but she didn't like my cats at all.
But don't make the cat live a life of fear - it's simply not fair to the cat. If you can keep her isolated for the dog, and her be happy, the remainder of her days is that fair?

Sorry for the delay in response.  Her litter box is in an area where the dog is not permitted.  I began re-babygating that particular room again like we had been doing for the first year and 1/2 of the dog's life so that she (Lucy) couldn't get in the room.  However, this is just a precaution, I really don't believe that Lucy has been going into that room. 
I don't think that the cat (Karma) is "terrified" of the Lucy, because she will confidently stand mere inches away as long as she's on the saftey of furiture which Lucy is not allowed on. 
But she is certainly Terrified of her if she's on the ground, where Lucy is allowed.  My guess is that she was blocked from exiting the bedroom when she really had to go.  I have begun closing the door to the bedroom while we are away.  There have been no accidents in 6 days and I have my fingers crossed. 
Other than that I don't know what to do.  I don't feel right about rehoming her....  I do really think she has it pretty good.  She lives on the couch.  She has a room to herself if she wants it.  She even has the option to go outside, which she used to LOVE to do when she lived at my parents house, but she has only been out since we moved to the new house a couple of times and not for a lack of an open door. 

Any other thoughts? 

perhaps try some Feliway spray (pricey stuff) see if that helps relax her. Other than making sure the dog doesn't bother her. She might lighten up after awhile. Usually if they are pooping on a bed they are sending you a clear message the only way they can.