Cat pooping outside litter box...

I have a 4 year old cat who has always been skittish since the day we got her, she takes off running if anyone knocks at the door, and takes off hiding when someone she does not know is around, afraid of certain noises, ect. Last year she started to crap on the bed when no one was in the room, then she would hide for the rest of the day. Then she would use litter box for few days to a week and crap on bed or under coffee table, she always uses litter box to pee. Her litter box is always clean, we scoop several times a day, whenever one of the cats use the box. We even added a second box in another room of the house. Litter box gets scrubbed out and clean litter once a week, along with new scoop. Took her to vet they did a compete examination and found nothing physically wrong with her. They put her on a 1/4 of valium once a day. This worked wonders up until a few weeks ago. She started to randomly crap on the bed and hide again, would use litter box for days then crap on floor somewhere, hide again all day, then be good for weeks, then repeat. There has not been any changes to her environment, she is eating, drinking, playing, affectionate, no signs of sickness. This morning, she went in the litter box, left a small turd, then she went into living room under coffee table was standing in position like she was going to crap, when she saw me she ran upstairs, minute later she ran downstairs really fast and hid in basement, i go upstairs and she crapped on bed! She hid all day, then when she came out of hiding she was back to normal. Does anyone know why she would be doing this, and what we could do to stop this? I am taking other cat to vet on Tuesday for her shots and will be telling vet all about this behavior.

Is she an only cat?  It sounds like she is not.  Is she declawed?  That could be a contributing factor to her general skittishness.  Obviously this is a psychological problem, but sometimes can be helped with physical changes in the environment.  The general rule about litter boxes is that you should have one more box than you have cats.  Another is to find the type of litter your cat prefers.  Dr. Elsey's Cat Attract litter works for most cats.

Some cats prefer to pee in one box and poop in another.  She is pooping on the bed for some reason, and then she hides all day because you are angry at her.  nce you get into that dynamic with a cat, ir's best to try to find out her background, and how she is with the other cats, etc. because until she is made to feel comfortable and secure, that behavior will continue.  

Cats who are on the bottom of the power grid at home often will poop beside the litter box rather than in it.  There are many things to know about litter boxes.  Here is an article about just that.  As for the psychological things, they are all tied into her past and present, and her relationship with you and with the other cats.  You need to become a detective and historian to see if you can find out what those things are, and then you will better know how to help her with this problem.  The first step is to stop allowing yourself to be angry at her, because that will make it worse.

http://www.thecatsite.com/a/how-to-solve-litterbox-problems-in-cats-the-ultimate-guide

She is not declawed, we do have another cat they get along great, we do have 2 litter boxes, what really puzzles us is that she will use the litter box to both urinate and deficate, same one, for weeks with no issues, then all the sudden she will start crapping all over, there have been no physical changes to environment, we never scold her, we treat these cat's better then most people treat their kids. No matter what they do we never scold them. We had her for four years and had the other cat for a year and 4 months. When we got her 4 years ago she was 6 months old and she stayed with her litter of 5 more kittens, along with mother and 2 other cats up until we got her. She seems to have no issues feeling comfort and secure, always laying on her back, affectionate, she gets startled very easy by loud noises, strangers. The latest episode of her crapping on bed happened right after she was on my lap, purring, affectionate, then she went to use litter box, left a turd, then went into living room I walked in she was squatting, about to crap under coffee table I did not say anything to her, she saw me and ran upstairs, minute later she ran downstairs very fast and hid in basement, thats when I found the crap on the bed.