This is confusing, possibly because of how you are trying to solve it. I think you are working too hard.
The intersection between two spheres is a circle. Unless you are just trying to plot the spheres, there is no reason to generate them completely. Just find the equation of the circle. MAKE THINGS SIMPLE. Don't overly complicate them.
c1=[0.2530 2.0740 0.2370];
c2=[0.2820 2.0920 -0.2870];
I presume that c1 is the center of sphere 1, and r1 the corresponding radius. Likewise, c2 and r2 are the center and radius of the second sphere.
First, do the spheres intersect? That is easy. I'll call D the distance between centers of the spheres, What mattes is the sum of the sphere radii.
D = norm(c1 - c2)
r1 + r2
(r1 + r2) > D
If that sum exceeds the distance between spheres, then there is an intersection. If the sum of radii is EXACTLY equal to the distance between spheres, then the two spheres touch at a single point.
We also need to consider the case where one sphere lies entirely inside the other? How can that happen? For that to happen, the radius of the larger sphere must be at least as large as the sum of the distance between spheres, and the SMALLER radius.
max(r1,r2) >= (D + min(r1+r2))
Had that been true, then one sphere would live entirely insode the other.
Given ll that, what is the equation of the circle of intersection? Also easy enough.
The center of that circle must lie on the line segment drawn between the spheres. How far? Assume the distance of the center of the circle along that line segment is d1 from the center of sphere 1. Then a little algebra tells me that
d1 = 1/2*(D + (r1^2 - r2^2)/D)
So, we now that the circle has center at a distance of 0.2916 units along the line segment, starting at the point c1.
circlecenter = c1 + d1*(c2 - c1)/norm(c2 - c1)
0.26907 2.084 -0.053446
The radius of the circle of intersection easy, it just comes from the Pythagorean theorem.
circleradius = sqrt(r1^2 - d1^2)
What else do you need to compute? The circle lives in the plane perpendicular to that line connecting the two sphere centers.
It is all just basic geometry, with an application or two of the Pythagorean theorem.