@Anonymouslyasking
Firstly, I'm sorry for your loss.
Have I got this right...
Your mum died first. She didn't leave a will. Her estate goes to you via intestacy laws.
Then your gran passed away. Some/all of the estate was to pass to your mother but as she has pre-deceased her parent it now comes to you.
The money being discussed here is from your gran.
As you well know, your half brother has no legal claim to this.
If my understanding is correct, your half brother also has no moral claim to it either, because your mother (who had apparently told him he would get half her estate) has predeceased her parent. Even if your mum had left a will. Gran's money would be going straight to you.
I think you're being extraordinarily kind to give him 25%.
You've said that you're scared he won't be in your life if you don't give in. What if you do give him 25% and he still acts the arse and cuts you off. Imagine how you'd feel then.
You've indicated the sum of money that 25% represents would be enough to buy a place outright. That implies it's 6 figures. That's way to much for someone that was not related to your gran to be getting.
If you feel you must give him something in order to appease your conscience I'd suggest 10%. And that's generous considering he's entitled to nothing.
You have 4 children to think of as well as the rest of your life.
You must put yourself first.
I'd also caution about spending too much of it on your dad's ongoing care too.
This money is for you and your descendents.