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Looks like, from the pic, you still need to cut the rest of that one rivet the rest of the way (only the center remaining). Then, yeah ..a punch like you're doing.
Angle grinder with a flap disc and clean that area up to remove the lip left from the rivet. It's still not going to be happy being driven out since it's puffed up/rusted into the wing on the ball joint but you just need to get it in far enough to go past the thickness of the control arm so it comes loose
M
Or even a small stone on a drill...might reach in there.
A die grinder with a good carbide burr like THIS, of that shape, on one of THESE, is a wonderful tool if you don't have one. Even on a cheap $12 die grinder. But the larger ones have more torque. Gives ya some reach. A good USA made burr will last 10 years or more of periodic use if you treat it right.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.