This sounds extreme. You said she passes out. Does that mean she loses consciousness or that she screams herself to sleep or.....? She whines while sleeping and wakes up screaming. How is this related to someone else holding her? Does she do this all of the time or just when someone else puts her to bed? Or are you suggesting that she wants you to hold her even when she's sleeping?
I don't have enough information to say this for sure but I suggest that you take her to the pediatrician and explain this behavior to him. It's possible that she has a medical condition that is causing this. The first one that comes to my mind is that she may have a sensory processing disorder. If this is the case, being held by someone other than you causes her nervous system to over react.
Has she always been this way and until recently you allowed her to dictate who held her? When she fussed you immediately took her back. That sort of thing. If that's the case she's learned that the more fuss she makes you will stop others from holding her.
Then I suggest that you do as LeAnne C. suggests. Start with short periods of time having her Dad hold her. Gradually increase the amount of time. Also, try using a blanket that both of you use when holding her as Jay G. suggests. I'd also try putting her in her crib with toys as MeganandOllie suggests so that you can get her used to be somewhere safe without you having to hold her.
Yesterday, a mom asked about getting her baby to hug and kiss is Dad. I suggest that you read that post and answers. Perhaps there is a reason that your baby won't allow her grandmother and Dad to hold her. Does she spend time with them so that she knows them? If not then I'd start with her getting to know them without them holding her. Are they harsh with her? If so, talk with them about how to be calm with her. Perhaps they should not discipline for awhile so that she can have a different sense of who they are.
Again, her reaction to other people, as you describe it, sounds extreme. I suggest that something is going on with her so that she doesn't feel secure unless you're touching her. Somehow you need to deal with her lack of security. I don't know how to suggest doing that because I do not know what life has been like for her. I strongly suggest that you get professional help.