This is a novel way to think of volcanoes erupting, and the book already has me interested. Unfortunately, lava (or magma, as it's called when it's inside the earth) does not come from the earth's core, it's actually from spots in the mantle. Now, I say spots because the mantle is not all fluid-y and full of magma; the mantle is solid, as is everything down to the earth's core which is molten iron. There are places, however, that have the right variables to create magma spots, such as the Hawaiian Islands.
These sites explain it much better than I can, probably because they've researched it and such:
The Short Version
The Long Version
I hope you can find a way to make this process work in your storyline!