Hi Teacake
Yes indeed, you aren't alone! Welcome to our online community Many of our members have BPD family-members as well and will be able to relate to you. I myself also have an undiagnosed BPD sister and know how challenging that can be. I am happy that you've already found this site so helpful in the short time that you've been here

I am sorry to hear your sister is in hospital now. Has she experienced psychotic breaks before and/or been violent to her husband before?
You ask if there is any way to get her husband to consider she has BPD. Have you ever talked to him about your suspicions of your sister having BPD. Your sister has been told she's most likely bipolar. It isn't uncommon that people with BPD get misdiagnosed as bipolar. Another possibility is that your sister has both disorders. BPD is known to be comorbid with other mental and emotional issues. Perhaps you can use one of these angles, misdiagnoses or comorbidity, as an angle to discuss your concerns with her husband and/or doctors.
People with BPD tend to be very sensitive and volatile so I understand your apprehension for contacting your sister. It might help to take a look at some of the communication techniques described here. I think they might help you better communicate with her or at least decrease the chance of her getting triggered:
Communication Skills - ValidationA 3 Minute Lesson on Ending ConflictDealing with the cruel things people with BPD say and do, can be very difficult. What I always try to keep in mind is that no matter what my BPD family-members say or do, it most likely isn't a true reflection of who I really am but more likely to be a reflection of their own inner turmoil and negativity that they are projecting unto me. This helps me not take their behavior (that) personally. Easier said that done of course, I realize that but I do find that it helps to keep repeating this to yourself and after awhile it did become easier for me to not take their behavior personally.
Also, recently she contacted me, apologised (first time ever) for things shes said and done and explained she felt a constant emptiness, knew she pushed away those who loved her, and felt like she was unable to love or be loved. Is there any hope?
There is! BPD is a very challenging disorder but there is hope. If a person with BPD fully acknowledges their issues and is willing to fully commit to better managing the disorder, it is possible for them to improve their behavior. Certain forms of therapy have been proven to be effective for people with BPD, Dialectical Behavior Therapy (DBT) is one of them. Have you heard of DBT before? You can read some more about it here:
Dialectical Behavior TherapyFor this therapy to be successful it is essential that the participants fully acknowledge their issues and fully commit to working on them. Knowing that, I'd say it's encouraging that your sister recently contacted you and apologized, this shows she at least has some insight into her behavior and how this affects others. Has she ever apologized to you before and/or in any way seemed to acknowledge that their might be something wrong with her?
Take care and I hope your sister's situation will improve