I don't know how you could continue to contribute 50% financially as both families have lost the whole of his salary however it was shared between them. It is unrealistic for you to still be able to contribute at the same level.
If he had died when still with his ex there would be no extra money coming in however she/her children may have had the financial security of the mortgage being paid off or life insurance.
Is the house owned or rented? How was it set up between you, who made what contribution? Was there life insurance? If he made no provision and I am guessing as you are posting here he didn't then personally I think his children would be entitled to a share his house. Unfortunately I don't know how this stands legally. As others have suggested can you make a provision for them to have a share at 16 or 18.
I also don't think you should have them 50% of the time. Yes they need to still have a connection with yourself and their siblings but you are not their parent. You need to work out a good amount and reduce over the next few months to something that is workable.
His ex is no longer in a position where she can be a SAHP and expect her ex to have the children 50% of the time. She doesn't get a choice. She lives on the benefits and a reduced lifestyle or goes out to work to support them herself especially as they are both at school. Just like you are.
What is clear is you cannot on a single salary, working full time as a single mother with two pre school children contribute the same time and money as you and your H were doing. If you carry on trying until you break then there will be nothing for any of the children.
It is a sad situation all round.
You are not in the wrong.