But the merged shape's corners wont go any roundier (Please replace that with a better word!)
You can use Live Corners to really quickly make shapes like these (version CC 2014 or newer). Use the Direct Selection or Lasso tools to isolate the corners you'd like to round then with the Direct Selection tool click and drag the Corner widget until the edge turns red.
More information on Live Corners:
I am gonna give you another way of doing this cause I find it easier to calculate rather than using lines with strokes:
Select the Rounded Rectangle Tool you already used, click anywhere on the artboard, give it a Width and a Height and set the Corner Radius to 890 px , this way, when you click and drag to create new ones, it will (if the height of the object is less than 1780px) always give the desired half-circle margin.
Go ahead and make another one and place it under it.
Create a simple rectangle between them with the desired width of the link between the two and the height equivalent to the gap between them
Take the Circle tool and draw two circles the exact same height as the rectangle .
Place each circle with the top-middle anchor point over the rectangle's top-left and top-right anchor points.
Select the two circles and the rectangle and go to Pathfinder > Minus Front.
Select all the remaining objects and go Pathfinder > Unite
If your goal is to make those shapes, you are going about it all wrong. You see how the rounded-rectangle shapes in the gif have rounded-edges of different sizes? You can't do that in Illustrator using the Round-Corners effect alone. It will try to force the same size corner on all different sized corners. Like this:
Here's how you do it right:
- Draw a line
- Increase the stroke
- In the Stroke window, select the middle icon next to "Cap"
- Duplicate your line. Change it's shape by changing the line thickness and/or shortening or lengthening the line itself.
- With your two lines selected go to Object >> Expand (make sure "stroke" is checked), hit ok. Your two lines should now be two rounded shapes.
- Add a rectangle that connects your two shapes
- With all three shapes selected, go to the Pathfinder window, and select the "Unite" button (first icon on the left, under "Shape"). Should look like the icon below. Now you have a single shape. Almost there.
- Draw another line with a rounded stroke. The distance between your first two shapes is how thick you want the stroke to be. Place the rounded corner of this line just over the connecting part.
- Duplicate the line. and move it to the other side of the connecting shape.
Select the two lines and expand them. (object >> expand)
Select all your shapes now
12: Go to the Pathfinder window and now use "Minus Front" (this should be the second icon under the words "Modes")
13: DONE! Ooh that's a nice shape you got there.
14: Continue doing this with different shape combinations and stroke thicknesses to build the earth. Cheers!