Stubborn dog stays on furniture when told to get down

She's probably not just stubborn. The reason she looks "guilty" is probably because she realizes you are annoyed, and so she's afraid or confused. Dogs are not actually capable of certain emotions, such as guilt. It seems she doesn't understand what "get down" means. Of course, dogs are not capable of understanding words unless we carefully train that word. When you say "get down" repetitively, she's just becoming confused, adding to the "guilty" look. (if you use "down" for the lie command, she may be thinking that's what you mean, and then not understanding why you aren't satisfied)

To teach "off":
Since your dog has learned that "get down" has no meaning, it may be helpful to switch cues, for instance: "off". However, you can still use the same cue, if that's more convenient. Don't use the command without enforcing it, or she'll learn it has no meaning. To start out, throw a treat on the floor with a sweeping motion, ending by pointing down. This will become your hand signal (for now, it should be a big, grand gesture, but you can make it subtler later). She will naturally jump down to get the treat (or toy, if she's toy-motivated). When she does, let her have the treat you threw, and then praise her. Make being on the ground more rewarding than being on the bed/couch. Repeat this as many times as necessary, then try just pretending to throw the treat. When she gets down, say your command, and then give her praise and a treat from your hand. Work for a while on getting her to jump off and giving the cue after the behavior, but then begin to give the cue first. If, at this phase, she does not respond, either gently lead her off the bed by her collar, or encourage her to come to you by acting excited. Don't use any other commands, but when she gets off, repeat the command, and say "good". Gradually simplify or phase out the hand signal.

Never try to push her off the bed/couch, as she may interpret it as a game, or even a threat. If you want, you could also teach her a "go to bed" cue. This will send her off your bed, and to hers. Make sure to reward/praise whenever she chooses the right choice on her own (getting onto her own bed or lying on the floor). If there are any times where you or a family member allow the dog onto a bed/couch/chair, it's just confusing her. Don't have conditional rules where she's allowed up if so-and-so is there, or if you're in such-and-such a mood. Make a consistent rule of not being allowed up- ever to help her understand what you expect of her. After she understands, you may choose to allow her up only by invitation, but be very careful if you do this, as it could result in confusion.

Supervise as much as possible, in order to prevent the behavior. When she seems about to jump up, redirect her to her bed, and praise her.

When you take her off the couch, don't leave her in a corner, she thinks you are punishing her for sitting in the corner on command, not for being on the couch. If you can say "no" as soon as she jumps up, she'll learn, but after that, you've lost your window. So if you walk in and find her there, get her off, as for an alternative behavior, (such as "go to your bed") reward, and then move on.

You have two dogs, then- if you use the same commands, do you use the dog's name before a command? As you probably know, unrewarded behaviors fade out. So, taking "sit" as an example, (though this perfectly applies to "get down"). If you say "sit" to dog#2, and dog#1 AND dog #2 sit, people generally reward only dog#2. So dog#1 learns that you don't really want a sit when you say "sit", becomes confused, or even learns that this is no longer worth her time. Or, with "get down", if you say it to dog#2 when dog#1 is not on the furniture, dog#1 becomes confused- "why are you saying that? I thought it meant to move from the furniture to the floor, but I am already on the floor..." They don't necessarily make the connection that you're speaking to the one you're looking at. I preface all my dog's commands with her name, even though I have only one dog, as an attention-getter. I use "Z, sit, come, etc." for commands, and "Kensi" when I'm just talking to her.

Also, is it possible that your original dog needs a "safe space" from the new dog, and that's why she's going on the bed? If the new dog ever goes on the original dog's bed, in her crate, etc., that should be stopped. The original dog needs something to just be "her space", so if she can't get that elsewhere, she may be trying to get the bed for that purpose. (Enforced "breaks" from each other, where they're crated separately, or one is outside and the other is inside, or one is getting 100% 1-on-1 training/play, can also help with this, as well as preventing anxiety or even, sometimes, aggression.)