本当は土曜日からの予定が、いろいろあって週明けからってことになった。

、。

It was supposed to start Saturday, but various things came up and it ended up being pushed to next week.

Literal

Really [topic-は] Saturday [from-から][possessive-の] plan [subject-が], various-things exist week-start [from-から][quotative-って] thing [to-に] became.

本当は…が 'it was supposed to be... but' sets up a contrast between plan and reality. いろいろあって 'various things happened' is a vague, face-saving explanation. ということになった 'it was decided/turned out that' signals a result arrived at through circumstances rather than individual choice — things just ended up this way.