I think its early days yet. From my experience it takes a lot of time and perseverence. Our first cat Winnie was a rescue cat. A few years ago we had to take my sons two cats Lulu and Suki [sisters]. I loved these two as much as Winnie so I felt I had no option even though I knew Winnie would not like it.
It did take a long time for them to get used to one another but eventually they did. For a long time Suki used to stalk Winnie, made her life hell, following her everywhere and ambushing her, poor Winnie had a rough time for quite a while especially as she had to get used to two new cats, thankfully Lulu was ok with her. Now, years later, sadly Lulu has passed away, we have acquired a status quo between Suki and Winnie. A few months ago we aquired Flash, a friendly neighbourhood cat who we had known of from a kitten. We grew to love him. When he showed up a few months ago he was suffering badly from a flea allergy, fur missing etc, it was obvious that he was being neglected. I was very reluctant to take in another cat because of the problems we had had with our other 3. To cut a long story short Flash has now settled down nicely and Winnie and Suki both tolerate him.
I think if you persevere you will get there, there were times when I thought it was going to be impossible but with patience Im sure it will work out. I think when Jasmine realises that Talli is a permanent fixture then she will eventually get her head around it and accept her. Jasmine is probably just telling her who is boss when she bops her on the head. She is probably a bit jealous too so you will have to make sure she gets the same amount of attention as Talli. They are both very young so will have lots of energy, I think its normal if one cat runs then the other will chase. I think when Talli realises that Jasmine is not going to harm her then she will start to stand up for herself and be less scared. It sounds like she is just needing to build up her confidence with Jasmine. When Jasmine chases do you reprimand her, I have found with ours that it helps because the inferior cat, Talli in this case will build confidence knowing that you are there to protect her and it will also give Jasmine a clear signal that her behaviour is not going to be tolerated by you. They are a bit like children really and need you to give them bounderies. At the end of the day you are the boss and you say what goes.
I think you are maybe giving up too soon, I think most cats given the choice would prefer to be the only cat in the household, I know thats true of mine. They will never love each other but they tolerate each other. I think your Jasmine and Talli will eventually but it may take some time. Like Gill said slowly slowly!
It would be sad if Talli had to go and be deprived of a loving home.
Good Luck and I really hope that you are able to keep Talli.