Hi there,
Newbie here, only my second post but have a little bit of experience so hoped I may be able to help.
First thing is that rescue dogs often have what is known as a 'honeymoon period' where they are taken home and seem like the perfect pets. Then, usually about 4-6 weeks after settling in, problems start to occur. Often these sort of problems can just stem from the insecurity of moving from their home/first situation to the shelter and then to another home and will settle down with consistence, love and patience.
Have you called the rescue centre you got her from. Very often they have their own or have links to behaviourists who can offer you some advice - also they will probably have come across most of these types of problems hundreds of times before and may be able to offer advice themselves.
It is unusual for dogs to foul their own beds - but not unheard of. I have a 10 year old bitch that started doing this when we moved house. We got through it with time, love and patience. We never scolded her for it (no point - she had fouled hours before we found it and wouldn't understand what she was being told off about) we just quietly cleaned up the mess and made sure we had done everything we could to eliminate it (early evening feed, extra late night trip outside etc). She got over it after a while (sorry I can't seem to remember how long exactly - but a few weeks) however she does revert at times of stress - like when we had to take in another dog as a rescue emergency. (She wasn't a rescue btw and had been living happily with us for 7 years before we moved.)
Only other thought is that our bitch is quite dominant and we wondered if she felt she needed to make her sleeping area in the new house smell of her as she had none of the usual smells etc from the old house around her. We thought that she also might have felt the need to do this to let the other dogs know to keep off 'her' bed. Our girl prefers to to have a crate in a quiet place, preferably under a table or with a throw over it but she absolutely hates having the door shut. If yours is similar, you could try keeping a large blanket on her bed during the day and then using it to cover the crate at night - thus creating a sort of doggie scented cave for her to feel secure in at night. (If you have washed her bedding in biological washing powder/liquid after the first accident and then again every time she fouled since then, her bedding won't be smelling very much like her by now.) Freckle was absolutely right about them returning to an area they've fouled before so while its important to keep the crate and bedding clean she may also need some of her own scent around to make her more secure.
Finally, if you feel the problems are stemming from insecurities you may find using a DAP diffuser helpful. This is a little plug in gadget that works a bit like an air freshener but dispenses the pheromone that lactating bitches give off to their puppies and works by relaxing the dogs. (The dogs can smell it but humans cant btw.) Many vet surgeries use them in waiting rooms and we use one from October through the end of November to get our collie through the dreaded 'fireworks season'. (All our dogs seem much more chilled out and sleep more at this time of year and it definitely reduces her sensitivity to the 'bangs and flashes'.) - you can google it as several online pet shops sell them and you can sometimes pick them up on ebay - they also do a spray version which we used when settling in a rescue pup - we bought him a bandana and sprayed it on that.
Well, sorry about the long post - but dog behaviour is such a complex area and it's quite difficult to give advice from a distance. Anyway hope I've been of some help and you get the problem sorted soon - I know its hard to deal with these sorts of problems but try to hold onto what a wonderful thing you have done giving this dog a second chance at happiness.
Good luck