Here We Go!!
OK, So it seems people may be over thinking things here, I'll just pop in to set the record straight.
Yoshi Games (Yoshi's Woolly World and previous) are spin-off games, so therefore they wouldn't have to take place in the same dimension as the Super Mario Franchise (main-series, SMB  through Super Mario 3D World). So, in an interview producer of Woolly World: Takashi Tezuka answered the question "Is Yoshi's yarn universe a parallel world to the Mushroom Kingdom, or did something happen to the Mushroom Kingdom to make it look like that?" saying:
"Yoshi's universe, both in the Yoshi series as well as the yarn Yoshi world in Yoshi's Woolly World, is separate from the Mushroom Kingdom. There’s not really a link between. " He most-likely did not mean that Yoshi exists separately from the Super Mario franchise, he just meant that because it's a spin-off game its universe does not have to co-exist with Mario's universe. Not to burst your bubble but not every Mario game is a game that follows the main-series, excluding Mario Kart which began adding characters from spin-offs (such as the babies) for a larger roster that would appeal to more players.