I'm afraid that the phrases you use in your post indicate that you really could do with a greater understanding of the differences between self-employment and employing people.
Putting it bluntly, a self-employed person does not have a contract of employment - they have a contract for the delivery of services. This is best described in terms of the outputs the contract should deliver - and the fewer the inputs that are specified, they better (as HMRC, if they get interested, look at the amount of control that the self-employed person has over the services they are contracted to provide).
So, for example, you could say 'provide personal care services to Mrs. P in her own home, supporting her during normal activities associated with living around the house and garden, by day and (where required) during night-time hours. The personal care services may include assisting with washing, dressing, preparation and cooking of food, feeding, use of the toilet'.
That's just an example I made up without thinking about it too deeply.
Would the contract for services also include domestic services around the house and garden?
The key with these things is to keep them simple and in output terms, avoid listing all the things the person would be expected to deliver, as by implication, if not listed, it could be argued it isn't included.
There will be some on here that will probably tell you that you have to have at least two clients to be self-employed; it certainly makes it easier to demonstrate self-employment if that is the case, though I do not believe that it is necessarily a requirement in every case. The nature of the support required means that you aren't after that sort of individual.
Have you thought about what happens 52 weeks of the year? - in a true self-employed scenario, it is role of the contract provider to source a solution when the contract-holder wants some time off (aka holiday).