I have a lot of experience of direct payments and employing a PA. You are certainly correct when you say its not easy to find one, unfortunately I also have to say its always best to find someone who is not a family member (generally it cannot be someone living in the same house as you) although the one positive is that you already know the person you are employing (a lot of councils have a ‘Find a PA’ website).
I have worked as a PA in two different local authorities and both strongly advised using an organisation to manage payroll and steered the person I work for towards that organisation. Adult services also pay the extra weekly charge made to handle payroll, so costs are covered.
One thing I would say is that the direct payments system works extremely well in most cases so good luck with it and finding a car.