If your son or daughter is not academic it might be worth considering a vocational option at a further education college. See government guide to find out about it. Although it is about full- time enrolment, it also covers home education options.
Grantham College takes students in year 11, ages 15-16, for courses to supplement home education. Click icon for their Home Education page.
Part-time college may be an option at this age for home educated pupils across a wide range of additional needs. Nottingham College has options for under 16s. Click icon for their Pre-16s page. It outlines options for years 9 – 11.
Nottingham College also offers options for participating schools to add a vocational dimension
Lincoln University Technical College has an admissions page for age 14. Click icon to view. Their SEND page encourages email enquiries. For more detail click SEND policy to download the full policy document.
Funding for 14-16 for college is provided by a national agency not the local authority according to Funding, so it looks like Lincolnshire pupils would be able to attend a Nottinghamshire college.
Here is a table of school years and ages.