Take her on lots of car rides.
It sounds like you already made the decision on the bed. I think it should work itself out with the cats. They may not want to be on the bed with the dog, and in my experience, dogs generally get too hot in the bed with people in it, so they scadaddle soon after people get in. Usually.
Only when Babs is in heat, then she stays in the bed ALL night Not sure why that is exactly.
Right now don't worry about anything but pottying outside. Training a day after you got a dog out of a questionable situation -- that is too much too fast, yes, even basic commands. And, if you want you can change her name. I use Eh! instead of No!
To get the dog to trust you, you need to give her space, and you have be calm and confident, and move deliberately with respect to how your body language is likely to affect her. I don't mean you are going to have to dance around her forever. I mean for the next few days, don't grab the collar, don't quickly pet the top of her head. Show her the leash, and ask, "Do you want to go outside?" Then bring your hand to her muzzle and reach from the side of the face to her collar and clip. Without using a squeaky, high pitched voice, say happily to her, "We have to put your leash on, if we want to go outside."
Do EVERYTHING matter-of-factly. You want her to gain confidence in you, and if you seem to know what you are doing, are consistent, and are calm, she will relax you and trust you.
I had to change my yelling at Frodo, because Arwen didn't like that. I did not want her to be afraid of me. Frodo could care less. You could hit that boy with a 2x4 and he would just think you wanted to show him a new game. You could yell, whatever. Arwen was different. She didn't like harsh tones or yelling, and ya know what? Neither do I. It is so much more pleasant NOT to yell. You certainly do not need to yell to get a GSD to mind you. Eh-eh, and then tell them, My Garbage can, you know you are not supposed to be in there, with your disapproving tone.
The voice is a spectacular instrument. It is an instrument for all occasions, and can be used for the whole spectrum of communication scenarios. Your dog is learning your tone as your language. This is good stuff. You need to learn what she needs, what makes an effective corrective tone that will not come close to shutting her down. What is an effective happy tone that will not put her over the edge.
Good luck. I think you have made a good start. Now just learn her.
Heidi Ho, Odie
Joy-Joy, Bear Cub, Hepsi-Pepsi
Cujo2, Karma Chameleon
Ramona the Pest, Kojak -- who loves you baby?
Tiny Tinnie, Susie's Uzzi, Kaiah -- The Baby Monster.