Power of Attorney is not easily obtained but, (purely in my opinion) having been granted to you, it does enable you to authorise all payments on behalf of your mother. Consequently, I see no reason why you couldn't buy a car from her capital.
The thought occurs to me that the purchased vehicle could even be registered in her name.
It will be interesting to hear some further opinions on this matter; ones which obviate becoming involved with the Court of protection.
Ron.