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Consequently, I have some unanswered question about the expansion of space. How can one distinguish between an object's velocity (movement relative to space) from space itself expanding?

You can't, for the same reason that you can't tell the difference between acceleration due to gravity when you're sitting in a chair at home, and acceleration from a rocket, when you're sitting in the pilot's seat. This is known as the "equivalence principle", and there are different formulations of it. It's a big topic.

Similarily, general relativity accounts for gravity due to space curving, but curving relative to what, meta-space?

Have you ever played the game "Asteroids"? If you move your ship past the left-hand edge of the screen, it appears on the right-hand edge; if you move your ship past the top of the screen, it appears on the bottom. The space in which the ship moves, therefore, is shaped like the surface of a doughnut. (Take a rubber sheet and connect the left-hand side to the right-hand side, and you get a tube. Bend the tube around so that the top edge mates with the bottom edge, and you have a doughnut.)

Now, when you're playing the game, where is the doughnut? In what space does the doughnut exist?

You can't, for the same reason that you can't tell the difference between acceleration due to gravity when you're sitting in a chair at home, and acceleration from a rocket, when you're sitting in the pilot's seat. This is known as the "equivalence principle", and there are different formulations of it. It's a big topic.

This is what bothers me. If they are equivalent, then how can we say the expansion of the universe is due to space expanding and not movement within space, unless we can distinguish between the two?

Now, when you're playing the game [Asteroids], where is the doughnut? In what space does the doughnut exist?

Why, nowhere but in the mind of the Person who Created the doughnut in the first place...

"Donuts. Is there anything they can't do?" -- Homer Simpson