I think you’ve been unrealistic and that it’s not affordable unless both you and DH increase your incomes.
You’ve implied household income is not a huge amount over £70k a year, which seems low to cover fees of £20k.
DH was previously on a low income - almost no income since last spring.
If fees are around £20k now, and would assume at least 3%+ increase a year. You live in London, which is expensive.
You have a younger child with additional learning needs and stated that you couldn’t afford private for him. Even if you decide private wouldn’t be best for him, help for DC with additional needs is costly.
Your DM has ‘offered to help out’ should you try to fund private for DS2. unless she’s extremely wealthy, with substantial funds set aside should she need care, it seems unrealistic that she could give enough to make it affordable. Such help could also be withdrawn at no notice.
Presumably your current biggest cost is housing. Having no car or overseas holiday could, for example, reduce outgoings by £2k (running a car) and £3k (example difference in costs between budget UK and overseas holiday) a year. Not enough to make a huge difference.