Lots to consider here....
On the one hand, if you are not working he is financially supporting your eldest child for whom he has no legal responsibility.
If you were on your own, you'd be having to live precariously on benefits if your only child (dc2 wouldn't have happened if your hadn't met your OH) couldn't go to school at the moment whilst waiting having to battle by yourself for a statement and more appropriate state provided schooling.
Would your previous job have enabled you to buy a home, if your first child had been able to go to mainstream school ?
You have considered your right to security if anything goes wrong, have you considered your OH's security ?
Whilst it would be good to make wills detailing what happens in the event of yours or your OH's death to make sure you are taken are of as far as any assets are concerned, wills can be altered later without the original intended beneficiary's knowledge so I wouldn't rely on that.
I think you are trying to close the stable door after the horse has bolted.
You are already in the position having had a child with someone to whom you are not married and being dependent on their goodwill continuing in respect of your other commitments (dc1). I don't really see how you can force them to sign away rights to assets they are currently sharing with you if they are not inclined to do so. He clearly wants to keep his financial risk associated with this relationship pegged to just child maintenance for your joint dc. Surely the signs were there when he didn't want to marry you before your joint dc was born.
I do think the only way forward is a compromise and agreement regarding a quite limited settlement if you split to reflect your stay at home period looking after his child.
I think the above probably sounds harsh but the reality of some people's situations can be just that at times