Finally - I wouldn't dream of telling my husband what he was and wasn't "allowed" to do with regard to parenting. Major decisions we make together but ffs, this is essentially 2 days out with Daddy plus one night in the middle. It's hardly a major parenting decision and if you told her she wasn't allowed to do something with her own child she would (presumably and correctly) tell you where to go!
I think that this is the major problem-why does she think that she is the 'senior' parent who 'allows' things? 
I'm sure that he is sensitive to his DW's feeling but it is unfair of her, she is the adult, it is her problem and it isn't in her DDs interests to have such a clingy mother. She may find it difficult, and be anxious, but she should hide it, especially from DD.
Have you asked her what would need to happen for her to feel comfortable about it? ie if you phoned every couple of hours, stayed away for one night the first time, she arranged to have a friend come over for company in the evening so she didn't feel like she was all alone if she thought that may be the trigger point for her emotions getting the better of her....
This makes her seem like some poor Victorian heroine who will take to her bed with smelling salts! Not someone whose DD is going to have a great weekend with cousins and fun household with the full attention of her father!
It at least makes her sound like an 8yr old who doesn't want to go to Brownie camp! She is an adult-just talk to her rationally and go! She doesn't need a friend to hold her hand and more than one phone call a day!
I agree with clam, if the DD is sensitive -all the more reason to go.
I'm sure that it gives some women a purpose in life to say 'my DC won't go anywhere without me' instead of saying 'how can I get my DC to go somewhere without me?' They don't like it is DC is completely a 'daddy's boy' or 'daddy's boy' (written about on MN plenty of times) so they should try not to have it the other way around.