Does the expanding universe mean that
Earth is at the center of the expansion?

NO!

Suppose the US doubled in size in an hour. 
Yellowstone is 500 km from SLC,
Albuquerque is 1000 km from SLC,
and Minneapolis is 1500 km from SLC.

Yellowstone moves away from SLC at 500 km/hr,
Albuquerque moves away from SLC at 1000 km/hr,
and Minneapolis moves away from SLC at 1500 km/hr

Cities that are twice as far from SLC move away twice as fast!

And everyone in every other city would get the same result!

Every galaxy in the universe is moving away
from every other galaxy in the universe.

There is no center of the universe's expansion.

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