Explain why global warming and the melting of North American glaciers produced an ice age in Europe?

This question is not entirely correct.

It was the collecting of large expanses of fresh water from melting ice, which was held back by thicker ice until it catastrophically broke through and entered the North Atlantic Ocean in one mass, causing the warmer sea currents from the south to be diverted.

This cooled northern Europe to produce a mini-glaciation, not an ice age.

Gradual warming would not have the same effect as there would be no large bodies of fresh water to add to the ocean.