That's not really the issue. OP's been very articulate and clear on her own needs or, rather, what she needs her daughter not to do. Unfortunately, the daughter is a child, for whom the message "I can't stand you hugging me" is undoubtedly harmful.
If she's been getting that message - non-verbally but kids aren't stupid - since the age of three or thereabouts, it'll be deeply embedded and she'll be feeling a cavernous deficit. Explaining that you need her help is just another way of telling her to suck it up, so please don't.
I know you said your baby's quite hug-averse, OP, which must be something of a relief to you! Toddlers need fairly constant attention, though, much of which involves touch. I agree on the probability of DD's feeling all the more deprived by comparison. If he doesn't want her hugs either, it's all adding up to an immense burden of rejection.
I enjoyed the Disney hug idea above.
If you agreed with PPs about bringing DD to a psychologist, I would hope you'd approach it not from a "what's wrong with her" point of view, but more of a "how can we fix our relationship?"