My Core Sucks

Pushups, timed  (not sure how long) x25. I think I misunderstood what I was supposed to do, I could have gotten more. Still managed 25 in a row which is more than I've ever done.
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45lb KB shrugs x100
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3 part bench x5
Bench / 45lb rows w/fat grips x5 ea arm
65lb 4/1 x5 / rows 
95lb 4/1 x5 / rows
115lb x5 / rows
135lb w/foam roller 4/1 x5 (light assist) / rows
135lb no roller 4/1 x1 (light assist ) / rows
135lb no roller 4/1 x1 (light assist) / rows
135lb no roller 4/1 x1 (light assist) / rows
95lb w/foam roller x10 (narrow) / rows, 3x
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Hang from swivel grips
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Hanging knee raise 4/1 x5 
orange band pull downs with a pause x20
Walk out/ hands up pushup / walk back in x5
H.K.R. 4/1 x5, band pull downs x20, 3x
H.K.R. x15
Band pull downs x15
H.K.R x10
Band pull downs x15, x10
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10lb (?) KB o.h. tricep ext x5 ea arm (assisted)
10lb KB o.h. tri. Ext (two hands) x10
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5lb shrug/tee x20
5lb shrug/front raise x20
5lb shrug/kick back x20
5lb front tri. Ext x20
5lb tee/Y x10 ea movement
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25lb shrug/hammer curl pause x10, 2x
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I'm pleased (sort of) with benching tonight. I'd like to see that 135lb getting up a lot easier than it is, but it will happen because I won't accept anything else.
What's bothering me most is the lack of core strength that I have. It's really pissing me off so my attention is being diverted to strengthening that area. A weak core just kills everything. 
Happy to have felt such a tight pump tonight,  a good burn going in my traps and having Justin tell me that I was getting a lot of muscles. Hearing that muscles in your back are now visible is a boost that maybe some people won't understand.  But to me, it means my work is becoming visible and if it's visible, it means there's progress. I'm even beginning to see some muscles separation on my thighs. They, however,  still have a long way to go. 
Confidence is there though. Along with determination and quiet drive.