Always a contentious issue, and we don't have all the facts, but...
If the debt really was joint, for a joint asset, then you are - at the moment - jointly responsible. So, as you say, you are effectively giving her �750pm. Future ownership of the debt will have to be sorted as part of the settlement, and you should get the part you have been paying, on behalf of your wife, included in the settlement. (Maybe you know all this bit, sorry)
As to your actual question, I don't think she has a legal right to claim it (if she left you) at the moment but it won't look very good in court (if it comes to that) if you haven't at least to some degree provided for your child. Surely you also feel a moral obligation to look after your daughter, also? Saying you're already paying �750 is a bit disingenuous, as your wife and daughter aren't seeing any of that. Isn't caring for your daughter the most important thing? How will you feel about it 5 years hence?
Why not offer �100 month, as an interim? Or come to a compromise? Though make any offer 'without prejudice'.