There's no "curriculum", but I think you have to work backwards from the "end game". If, for example, you intend to educate throughout, right through to aged 18, you need to be working to an end-goal which is a job, or university, or apprenticeship, or whatever. Obviously, when your kid is just 2 or 3, you've no idea what that end goal is, but you know that by aged 18, they need to be ready for the adult world or work or further education. Alternatively, you may only intend to home educate until the age of 6 or 11, or whatever, and in that case, you need to ensure you'll have covered whatever fundamentals are required by then.
Whilst you have a massive amount of flexibility, you have to look at the long term. That means Maths & English as a bare minimum, probably with a fair mix of science and humanities alongside. That's just to give your child a good grounding. How you "teach" them is up to you. Other subjects are more optional and subjective, such as Arts, music, drama, sport, cooking, woodwork etc - you can do a lot of "low level" fun activities covering those areas from a very young age, and there are usually lots of non-school group activities than can be done, such as dance schools, activity centres, sports clubs, etc.
Ultimately, if your children are to get decent jobs, they need a good set of GCSEs including Maths & English as a bare minimum. How you get them there is up to you and where you move from "home" to real school likewise up to you. But it would be a massive detriment to your children if you didn't plan it all out and ensure that they get the qualifications they need to make them happy in adult life. What that means will depend on the child, their ability, any disabilities, etc etc.
As for there being no "control", well no there isn't, but surely any decent parent will do what's best for their children. And any parent who doesn't give a toss probably wouldn't care whether their kids go to school anyway, not care about their behaviour at school, etc etc.