Gaming Lounge

[Kriven]

The way it was meant to be?

If that means you're trying to do it all in chronological order, Yoshi's Story and Touch 'n' Go both come before Yoshi's Island DS.
And if you're really counting Touch 'n' Go, there's a slew of other Yoshi spin-off games in there as well.
Counting all the Yoshi games:

Yoshi (NES/GB) - Yoshi's Cookie (NES/SNES/GB) - Yoshi's Safari (SNES) - Yoshi's Island (SNES) - Tetris Attack (SNES) - Yoshi's Story (N64) - Yoshi Topsy-Turvy (GBA) - Yoshi's Island DS (DS) - Yoshi's New Island (3DS) - Yarn Yoshi (Wii U)

I left out anything where Yoshi is not the main character and ports.

If you want a vaguely canonical order:

Yoshi's Island/Yoshi Touch 'n' Go - Tetris Attack - Yoshi's Island DS - Yoshi's New Island - Yoshi's Story - Yoshi Topsy-Turvy/Yoshi/Yoshi's Cookie - Yarn Yoshi