how do i get my rescue cat to cuddle and like to be held??Also she has a broken tail, and was super scared , was she abused?

I agree with the other person who has suggested heated blankets and treats.

Keep in mind that not all cats are cuddlers.

We had a cat who was a feral cat at age two. At first she would not even come out from under the desk to eat. We kept her in a small room where she would feel safe, and then fed her twice per day. We had to put the food under the desk at that point.

Eventually, she came out of hiding to eat in our presence, which was a very big step for her. I began using words to describe what I was doing. That meant she had a way to predict things in her life.

The very first thing I did to introduce her to human interaction was to allow her to sniff my finger. I used a word for that so she would know nothing else would happen besides her sniffing my finger: "Sniffy-sniffy". She accepted that.

When I began touching/petting her head I would say, "pet-pet". She knew that was all I was going to do and she was safe. I actually could only touch her head with a long mixing spoon at first, using that same cue. Then, we moved to my hand after some time and she accepted that - but I used her comfort level as my guide.

Any additional actions needed a word, AND TIME for her to accept and become used to the action. She now sits next to us and purrs, and even demands attention as a normal house cat would, walks across the lap-top, and across any papers I am working on! She is a happy cat and "smiles" with happy eyes and the way a cat shows it is happy. But, this all took time.

You need to gain a cat's trust. If you are carrying the cat around because you like this, the cat is not going to feel comfortable with you, nor feel you respect her boundaries, if she DOES NOT like this. Our adult daughter can carry "Aunt Kitty" around sometimes, but she apparently likes our daughter, and this is only a brief interaction. Some cats who were not carried and fully socialized as kittens simply will not be cats you can carry around on a routine basis.

Teach this cat cues for each thing you are going to do; respect her boundaries; teach her a cue for lifting up and/or cuddling and do this only a little at a time, AND let her back down when she shows this is what she needs. Respect if she does not want to be held or does not want to cuddle. She has preferences, too. She will also have things that still frighten her if she was not truly socialized before she came to you. Please respect that, as well.

If she still seems jumpy, then give her a space where she feels safe, such as a small room where no one will bother her. You could also purchase a tall cat tree, because many cats and especially shy cats feel safe on a cat tree where they can observe things around them. It can take a lot of observation on the part of the cat and especially as they watch the other cats and what those cats accept. Some cats are fast to catch on, and others take quite awhile.

I would not carry this cat around, if that makes her uncomfortable. I would suspect this is a formerly feral cat, or a cat who did not have a lot of human interaction/socialization before she came to you. Respect that and give her time to do things and "come around" on her own terms. Trust is a big deal and important. 

Additionally, if any of your cats frighten her, this would affect the whole outcome. If any of these cats are not neutered, this would also affect things. Get everyone spayed or neutered.

I find it so funny that nearly all feral cats I have come across usually get along with the dogs almost better than the humans, if the dogs have been taught to respect cats.

Broken/missing tail tip: Who knows; it could even have become frost-bitten, or broken off from getting caught in something. Poor kitty!

all kitties love heated blankets put one on your bed and show it to her, and when you give her treats pet her while she eats them, another thing you can do is maybe have a safe place for your cat to retreat to when scared