The correct interpretation of the expansion of the universe, analogous to your solid ball scenario, is that the distances between all the galaxies will increase throughout the ball.
As the ball gets bigger, the fabric of space itself is expanding, which causes the distances between all galaxies, regardless of their position in the ball, to increase. This expansion is uniform and affects galaxies at all locations, leading to an increase in distance from one another. The underlying concept is that the space between galaxies is stretching, which results in a redshift of the light from these galaxies as they move away from each other. So, the first option is the best representation of the situation.