Cat Behavior - Bad Manners or afraid?

6 months ago I adopted a black cat from a rescue shelter. She is a beautiful cat and she was skittish when I brought her home but I thought after acclimating to our home and seeing how happy our other 2 cats were, that she would warm up to us. Well she hasn’t. At first I thought she was scared because she had possibly been mistreated at her previous home or somewhat feral but her odd behavior contradicts these explanations. She easily runs to us when she is hungry, meows and talks to us, but then as soon as we reach to touch her she runs. She only comes to us when she is hungry. She seems to want to be close by, but doesn’t want to be touched. She is about 4 years old. Can her behavior change? Can she be trained to be more affectionate? If this was the only issue we could possibly ignore it, but we can’t even get close enough to her to cut her nails or put her in the carrier for vet visits, which makes her unsafe to our other cats who get groomed weekly and are up to date on all their vet visits. Also, we adopted her because we thought she would be a good companion for our two boy cats who are real lap cats (they act more like needy pit bulls than cats), and she is like a fish out of water here and I feel sorry for her but I can’t jeopardize the health of my other babies. Any suggestions?