This is, usually, quite an easy fix it just takes time.
I’ve fostered for large breed dog rescues and a couple of bulldog rescues and have experience dealing with anxious dogs. Although I do not pretend to know everything! My new rescue has definitely put some new things my way, but here’s some bits that work for me.
Firstly, they need a routine. Routines help dogs feel safe, the more they get to know they get fed at 9 walked around 12 fed again at 4 the better they become. This is one of those things that take time. Eventually, they’ll be able to be more flexible in their routines once they’ve established that trust but initially this what they need to do. Rescues take time, it’s a scary period of settling in for them.
Secondly, your sister sitting with the dog all night is not helpful. For me, it reinforces the dogs anxiety. What would be helpful if she finds your sister presence reassuring is leaving a t shirt that your sister has worn with her overnight, this works wonders. Your sister won’t be there every night it isn’t realistic.
A PP mentioned a snuffle mat, great idea absolutely love them. Can be quite easy once they understand how the game works so brain games will help. But take the dogs cues, any kind of avoidance or mouth licking might mean they need a break. Short little spurts are best initially and will develop their bond.
Also, I’ve always left my rescues well alone. I set them up a nice little spot with whatever they come with, for example one came with a beach towel so I left her with her ‘familiar’ scent. They have their own water and I just let them be. If they want to come for a cuddle/a play that’s great but sometimes they need time to just learn the new environment in their own time.
I also highly rate thunder shirts, one of mine has one on her walks and she loves it. Makes her happy and approachable, immediate difference. Get the thunder shirt brand not the cheaper ones though.
My mastiff, currently curled up on me, shook for a week when she came. She’d never been in a home environment and everything was so new and scary. It was helpful that I had another dog that was just so happy with life so was a calming influence. I definitely think I would have freaked her out if I’d pushed her too much initially.
Rescue dogs are hard work and do present challenges, but without doubt they are one of my biggest achievements. So please let your sister know it’s a hugely worthwhile endeavour! There’s absolutely no shame in asking for help either, she should have a support network from the rescue and maybe join some FB groups for advice.