The sheep and the wolves
It sounds like you're describing Fox and Hounds here:


The four Hounds can only move forward diagonally.
The Fox can move forward or backwards diagonally.


There is no jumping or capturing involved; the Hounds win when the Fox can't make any legal moves, and the Fox wins if it reaches the far rank (where the Hounds started).

This game is inherently unbalanced; with perfect play on both sides, the Fox (aka the Sheep, in your case) cannot win. I find it likely that, as a child, finding the game "sufficiently challenging for both sides" was more due to your inexperience in recognizing the optimal plays than in any house rules that actually balanced the game.