Christ's sacrifice was ordained from before the beginning of time. All creation leads up to the empty Cross; all history flows from the empty Cross.
That's why it's no small thing to be shown this fact, and dismiss it.
There's the first item of substance I've noticed you get right. :-)
Yes, when people debate "the Jews killed Him" "no the Romans killed Him" some Christian will point out "no, our sins killed Him" and it will eventually hit home to all "I killed Him".
While all of those things are true - and the later are necessary realizations to come to - there can be no doubt that God did it. And knew that He would do it from the beginning of time.
All of which, of course, is irrelevant to this particular discussion since the debate is over what "it" is and how it could be "finished" at calvary if the sacrifice was accepted today. Your post would serve to defeat mom's point.