Sometimes I wonder if you've been watching the same tv Show as the rest of us.

Watch the WHOLE CLIP I posted below and ask yourself if Tywin
'took no pleasure' in what he did to the Starks at the Red Wedding.
I never spoke about every combat officer in Vietnam, Dessert Storm or Iraqi Freedom.
I was only talking about Tywin & Cersei... 2 Fictional TV Characters. NOT real Soldiers.
Watch the WHOLE CLIP I posted below and ask yourself if Tywin
'took no pleasure' in what he did to the Starks at the Red Wedding.
From the
4:00 min mark to the
5:30 mark... Tywin is VERY
'proud of himself' & what he accomplished.
So Yes, I'd say his
'pride' and
'smug demeanor'....... is equivalent to
'taking pleasure' in the violence.
His smug attitude.... is quite sadistic.

That's EXACTLY where Cersei gets her attitude from.
But she takes it to 'new heights'.
Tywin gives you..... a slick 'smirk behind closed doors'.
But Cersei gives you..... 'visible enjoyment written all over her face' in public.
But they BOTH are 'taking pleasure' in their sadistic actions.
^^ You are wrong about all of this.

I suspect you are confusing alot of stuff you read in the books.... with the actual TV show.
Tywin was never
'shocked' by the outcome of the Red Wedding.

That was the outcome he
INTENDED to happen from the very beginning.
Yes, Tywin ABSOLUTELY ordered the
'wholesale slaughter' of the Starks.... at the Red Wedding...
in complete 'violation of host rights'.
The Stark forces had to take a 'time-out' from fighting in a War.... to hold a 'wedding ceremony' for 1 day.... so they could cross the Frey bridge the very next day... and go right back to fighting a War again.
So in the midst of a War... that Wedding was the ONLY location (and time) that Robb & his whole Army would ever
'let their guard down' long enough to get caught slipping.

And Tywin knew it.

Because he KNEW Walder Frey would have absolutely no problem having a 'despicable reputation' for violating 'host rights' attached to his family name... if it meant he would control the Riverlands.
Btw, here is the whole scene when the Small Council discusses the aftermath of the Red Wedding.
When Tyrion says
"They North will never forget this"... just wait for Tywin's SAVAGE-ASS response.

Then ask yourself whether or not.... he is a 'murderous bastard'... right down to his Bone Marrow.
If you think Tywin DID NOT KNOW that the Mountain would rape that Martell woman.... You're crazy.
That's like saying...
Tywin ordered Ramsay Bolton to kill someone.... but he had NO IDEA that Ramsay would actually FLAY THEM also.

C'mon, man.

He absolutely knew.
Tywin knows ALL the violent habits & heinous brutality his Bannerman are capable of.... Especially the Mountain.
Watch the clip I posted above. Start at the
5:30 mark.
He suggests to Tyrion (in-a-very-indirect-manner) that he should probably "Rape" Sansa, to produce an heir.
That scene ALONE should tell you that Tywin HAS NO QUALMS AT ALL about ordering a 'Rape'.

Either directly. Or indirectly.
You're not watching the same show.
Tywin was never FORCED to sentence Tyrion to death.... because Tyrion should never have been ON TRIAL in the first place.

Tywin could have SILENCED all of Cersei's
'false accusations' right on the spot.

if he wanted to.
But he chose not to.... Because he saw it as a golden opportunity to kill Tyrion after holding a 'rigged trial'... and REMAIN BLAMELESS.
If you think Tywin (for one second) ever had ANY REAL INTENTION of actually 'sending Tyrion to The Wall'.....
"You haven't been paying attention." - Ramsay Bolton