Connecting two Circles With a Body

See the image for a complete understanding. I’m trying to create a curved body that connects the two circles. As you can see, on one end the shapes are tilted while the others are not. I’ve tried a sweep along the line I drew but it does not meet with the other circle correctly on either end. The ends don’t match the angle of the other two shapes and ultimately come too close together to work properly and they’re both spaced exactly as they need to be. Replace face won’t work because there’s no body yet and if I tried doing that it’d give me a truly odd result. There should be a way to sweep between two shapes and have it follow a curve to the place on the axis where the connecting shape exists.

Any suggestions on how to do this the way I need to do it?

I would use Sweep and Subtract.
Use one circle and the line to create a sweep, but first make the line longer than needed. Temporarily hide the new body. The other clrcle is on a separate plane and is askew relative to the 1st circle, right? On that plane, create a body like a cube larger than newly created curved cylinder. Unhide the curved body and subtract the cube.

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Try putting some (depending on how smooth the curve should be, maybe quite a few) intermediate circles perpendicular to the line, then “loft” might do what you want.

Yes, like Steve says use the “Loft” command to connect them.