What does the machine do when it cuts? Say it starts top left of the outside contour and goes clockwise. I suspect it might go right, clockwise round the right hand semi-circle, then left along the straight bit at the bottom, then straight up (which is wrong) then anti-clockwise around the left curve.
What does the contour look like in your CAM program? Does it show as a closed polyline? Can you display 'span directions' for each segment?
One thing you could try is to explode the polyline that forms the outside of the shape and then do PEDIT, JOIN picking the entities strictly in the order you want them machined.
It is, as others have said, a CAM problem not a CAD problem.
EDIT: the small oval seems to cut OK. Copy, rotate and scale it then delete the big one.