How to fix bearing cup for fixings loose wobbly wheel hub of old bicycle?

I have watched videos for Bicycle Freewheel Disassembly/Assembly, and disassembled my damaged bicycle. The back wheel of it started to Cranking, and by opening its part based of this video instruction:

I have bought one ball bearing for it, but it seems not fit in its hole as you can see:

Also you can see below that,there is some corrupted part inside the hole which I guess there must be something inside it like which I understand it is broken and detached to two part as you can see below:

So, if possible, I want to know how can I replace bearing cup(sample photo of cup, but not my case!)? Maybe by removing the bearing cup of other side or something else.