"I don't know how they could turn a child away without even dressing his wound."
Joshua had two operations including a skin graft, and is still being cared for in Alder Hey.
The accident happened as Joshua, from Liverpool Road, Huyton, crashed on his new mini-motorbike with brother Callum, 14, on Southport beach.
Ms Madden said: "It was terrible. His leg was hanging off. Joshua was hysterical. His leg looked like a shark had bitten it."
Her partner David Lewis, made a bandage out of his t-shirt and took Joshua to Southport hospital - to be told to go to Ormskirk.
A spokesman for Southport and Ormskirk Hospital Trusts said: "If a child comes in they will be assessed and advised about the best care, and if necessary they will be stabilised here."