If you have a set of sockets, you can use them to press the cups out of the yoke. Select one to use as an anvil that the cup will fit inside, but the yoke around it will be supported and another that's slightly smaller than the cups to punch it out with a hammer. Not the preferred use for sockets, but it will work. Back in the day, GM had an old filmstrip featuring Primitive Pete abusing tools.
Or you can rent/borrow a ball joint press from most parts stores. That's really the correct way. Like this
Kevin 1951 Chevy 3100 work truck Follow this saga in Project Journal Photos 1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car) Busting rust since the mid-60's If you're smart enough to take it apart, you darn well better be smart enough to put it back together.
I have used a heavy duty steel C-clamp (I think it was a 6" opening span) and 2-6 point sockets (they have thicker side walls) sized like Kevin noted in his reply to press the cross shaft and bearing cups out. You could clamp the C-clamp into your vise (in your picture) to hold it steady while turning the adjuster to act the same as the "ball joint press". The C-clamp set-up still acts like a press, so removes the chance of miss-strikes with a hammer.
Just a thought and hope it's helpful. Let us know what you figure out.
~ Dan 1951 Chevy 3 window 3100 Follow this story in the DITY Gallery "My Grandpa Carl's Truck and How it Became Mine" 1966 Chevelle (Wife's Hot Rod) | 2013 Chevy Silverado (Current daily driver) US Army MSG Retired (1977-1998) | Com Fac Maint Lead Tech Retired (1998-2021)