So I've had my rescue cat for nearly a month now and she still does not like me at all. If I go to touch her she will hiss and growl most of the time (sometimes not at first but then will once she realises that I'm the one touching her). She allows older people to touch her, both myself and my partners mums. She allowed the vet to touch her and even scratch her bottom back tail part (which she hates when my partner does it). So I found this so strange. It's like she just doesn't like me or my partner as if it's because we are younger. (22). I don't know whether to give her even more time to get a bond going or to just take her back since she's miserable with us? I didn't rescue a cat just to look at it and have it hate me.
You haven't stated in your posts; have you had a cat before?
When we got our first cat he avoided us for a month or two, he was totally different than he was at the shelter. Honestly the thing that helped the most was to ignore him and give him space. When he was ready he started coming to us on his own and cuddling, but not allowing petting. Then he slowly allowed petting. Now he cuddles so hard you can't stop him. So maybe try just ignoring her until she's super comfortable with you.
mhwombat posted a lot of good links and resources to try as well. My Cat From Hell is a good show to think more like a cat, he emphasises playtime which helps a lot of cat problems.
I'm so sorry that you're having this problem. As a tip for the future, when you adopt an animal, choose one that is friendly toward you and is OK with being petted by you. Don't choose an animal based on its appearance or breed. Ask the staff about the animal's personality, and tell them what you want in a pet.
A good shelter will make sure each animal is socialised before making it available for adoption. If the animal has specific issues (e.g., is nervous around noisy children), they will make sure that the animal goes to the right type of home and that the potential owner is aware of the issue. So if you decide to take this cat back and adopt a different one instead, don't feel bad about your decision.
My guess is that the reason this cat is more comfortable with your mum and your girlfriend's is that they are more experienced with feline body language, how best to pet a cat, and most importantly, when to stop petting. Maybe you and your girlfriend don't have as much experience with semi-feral cats. Or maybe you remind the cat of someone that was unkind to her.
It should be possible to turn this cat into a more friendly, loving pet, but it will take work. This video You're Petting Your Cat All Wrong! from Jackson Galaxy should be very helpful. If you're patient, and persistent with these suggestions, I think you will be able to make a big change in your cat.
I also suggest that you watch the TV series "My Cat from Hell" with Jackson Galaxy, particularly the first season. Some of the series is on YouTube, but it would be worth purchasing the DVD set. You'll learn to see things from a cat's point of view, which will help you solve the problems you're experiencing.
Here is a link to an excellent short series of videos on socialising feral cats. Not that your cat is feral; in fact I think you will see that you've made more progress than you think.
The gist of it is using food and irresistible treats to get the cats to eat in the presence of humans that are far away; then eventually requiring them to eat in the human's lap. You will need to move forward in very small stages. Best of luck to you!