Open Question: Need Solution to Cat Problem?

Just over 6 months ago we moved house & we brought our two cats along with us, both are of a mature age.
At our previous home the cats had access to a cat door to let themselves outside to do there private business. We NEVER had a problem with them inside, we didn’t even need kitty litter.
After we moved, it hasn’t been the same since. Moving the cats appeared very difficult for them & they didn’t enjoy the car trip at all. After arriving one of the cats has adjusted fine & now uses kitty litter; but the other has had some troubles.
She only used the kitty litter once or twice but the rest of the time she went where she pleased, we tried numerous techniques such spraying areas with citrus, but she just kept on.
Now she lives out side and in a room that connects to it, most of the time she is kind enough to go do her business outdoors but every now & again she will just do it in her own bed!!!
Is there a solution?
Please help!
Additional information: its never seems to be urine just ‘solids’ that she leaves behind.
Yes she does have access to a kitty litter tray & she has own easy access outdoors.
And she definitely didn’t hold it on the trip up; very smelly car ride!