However I would expect more in the way of qualification or experience than is being asked for.
...... but you say the salary is a very basic one. You said 12.700 (not sure if you are saying £12,700.00 pa, or £12.70 per hour, but either way, the salary is not going to attract highly qualified people in the main, unless you just hit lucky as it seems you did in Primary school with someone wanting short hours, term time only. So, with such a low salary, why would you be expecting "more in the way of qualification or experience" ?
Now, don't get me wrong, I know SEND support is incredibly underfunded, and I also get that personal care such as this is a very sensitive area, but I agree with everyone else that you can't apply for the job.
My concerns only relate to getting off on the right foot and giving DC the best chance of success in secondary.
My tip would be to be pleasant and helpful to the school and communicate with them in a way that says "How can we make this work....." rather than "I am going to / not going to"
Also, to be a bit more honest about what you are asking.
This thread has nothing to do with whether a teacher can teach their own child at school.
It also took you several pages in before mentioning a pretty crucial piece of information that your dc's 1:1 wasn't leaving, but that your dc was going to a completely different school, which will (as a secondary) obviously work in a completely different way from the current (Primary) school.
Be clear what you are asking about at all times and you will get clearer answers.