I think your squeamishness about having your cats do their business inside the house is causing most of this problem.
First problem: the "training her to go outside". To me that's a dog thing, not a cat-thing. She's not a dog, don't do that.
Second problem: Too few boxes, and too dirty. The rule of thumb is: one box, per cat, per floor, plus one. 2 cats, 2 floors, should mean 5 boxes, not 1. Rationale for this: 1. Cats can't be counted on to go upstairs from downstairs or downstairs from upstairs when they need to go. 2. Cats many times want a "poo box" and a different "pee box". So if there is poo in the box, your duvet becomes the pee-box. 3. If you think that a litterbox seems smelly to you, imagine if your sense of smell were 7x what it is (that's how good cats smell). If your cat is having "litterbox problems" and there is any suspicion that it is due to rejecting the litterbox, you need to keep it (them) a lot cleaner than every 3 days!
Third Problem: Getting booted from the bedroom. The bedroom is usually pretty sacred ground to cats. So being sometimes let it, sometimes not, something having their humans cheesed off at them etc., that alone can cause stress, and stress can lead to litterbox problems. I get it that it's stressful to you too, but understand that to solve this you probably need to reduce the stress on your cat.
My suggestion is: 1. add the extra boxes, keep them really clean. Put a litterbox next to where her "hot spots" are (where she goes inappropriately) 2. Get some feliway plugins. They are for cases like this. 3. make sure you are playing with your bengal every day. This reduces stress and lets her know you are still "buddies". 4. Extra catification (cat trees, cat shelving etc), although it seems unrelated, can help. Again, it makes cats feel more confident and have special places that "they own".
If you continue to have problems, consider seeing a cat behaviorist. I'm sure this is probably the #1 thing that they have to deal with. You can't be a cat behaviorist and not have a really solid gameplan for handling situations like yours. It isn't that uncommon.
_________________ The little monsters 3
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