I am sorry to hear of your wife's reaction to the toothpaste. Did you try it, and did it affect you?
The "goods" have to be "as described" (which they were) , and "fit for purpose". You are saying that that they are not, in view of your wife's adverse reaction. The problem is that individual allergy responses vary.
My wife went to an allergy clinic about reactions to skin and hair products, and now we avoid some brands that contain a particular preservative. I have discussed this with manufacturers, and their stance is that the products are suitable for the vast majority of buyers. Also, we buy "non bio" detergents for the same reason. If we use "normal" biological detergents my wife gets an allergic rash, but we do not ask for a refund as we realise that my wife is in a small minority.
I think that if your wife is in a similarly small minority (ie most people are able to use the toothpaste with no issues) then in law you would have a difficult case. I suggest, if this is a wider problem, that your wife is referred via the GP to an allergy specialist who can suggest ingredients to avoid after testing her.