Hi Amanda,
Don't worry I know your new bunny Primrose seems unhappy but with a bunny companion and in a home where she is not being frightened or terrorised by dogs/children she is probably a lot happier than she has ever been
The problem is that emotional damage done early takes an awfully long time to overcome, it can take years, and it might never be that she fully trusts you but that doesn't mean you can't make any progress at all. The wonderful thing about nervous bunnies are that you learn to be grateful for the tiniest things that other buns will do with no trouble at all.
I know exactly what you are going through, our rescue girl was identical to this and would cower the minute you move towards her, she is terrified of people. We've had her nearly 2 years now and she is such a changed bunny, although she is still nervous at times so you have to just be really patient i'm afraid.
From our personal experience we have found that the best way to deal with this is to lower your expectations and you will be pleasantly suprised by the little improvements your bunny makes. It can be very frustrating I know, just remember that it is not anything necessarily that you are doing now, she just remembers negative associations from her life before and this is instinctive, she has learnt to behave in a certain way to protect herself, it is no reflection on the care you give her now, but certain things we have to do like pick them up daily, will of course reinforce their experiences. The difference is that she will learn nothing bad happens to her and eventually she will make new associations in her little rabbity brain, but it takes time.
Having a bunny companion should really help her so you've already done that for her. I can't tell you the number of times our bun's bonded companion has given her the confidence to try new things and explore new places, and even to trust us. She used to watch him bounce all over us begging for a treat and now she's the first to arrive! Initially we couldn't voluntarily touch her at all, then she began to let us touch her nose, and just a month ago her back for the first time in 2 years! A daily brush is another good bonding technique for you and her. You have to stick at it and be consistent and calm. I totally agree with the passive presence technique, just try and be around her as much as possible in a passive way, read a book on the floor for example. We find lying on the floor flat and just talking to our bun makes a huge difference.
We also found that nervousness is heightened when she is tired or just woken up.
Routine is essential for a nervous rabbit, they need to know what to expect and when, and this can help enormously with the trust issues. I know you have to pick her up daily for a health check, i would try and find the least stressful way to do this for her, we found our girl would feel happier being picked up from the litter tray, somewhere she feels safe. I'd avoid any chasing or activites that might put her into 'fight or flight' mode and use treats as a reward following any contact you have with her - healthy ones obviously, as a starting point. I hope that helps a little. Just be patient, she'll get there in her own time