Ah, I see.
Under intestacy rules, the estate is split equally between those children living at the date of death, so the estate of child 1 in your second sentence gets nothing.
If a child of your mother died before her but left three children, they share the proportion that their parent would have been entitled to.
So the estate is split 5 ways - 20% to each of 4 living children including yourself.
The remaining 20% is split equally (6.66% each) to the three children left by the one who predeceased your mother.