Eli:
As tempting as it is to use SW stance and stay close against Yoshi (speaking from experience here), CL range is your best bet against him. He has virtually no mixups here; the only options Yoshi has at this range is a no-big-deal B, a punishable lunge (forgot the notation for this; the move where Yoshi dives towards you) and a punishable CR 3K. Granted, 3K is hard to block, but you get 30-60+ damage punish versus his 20-30 if you don't block it.
Edit: Forgot that he has that instant aB slash here. But this is a high; mainly use CL 6B/33A to dodge and attack.
At SW, I find that Yoshi outclasses Ivy in the mixup department. iMCF pretty much beats everything Ivy has and IS safe. Dragonfly shenanigans work best close range too. A+B[A+B] unblockable isn't as effective against him either, given his instastep. Best bet here is push him away to CL and pressure him from the outside-in.
You got the idea of what to do when he knocks you down; take the dragonfly sweep/2k and tech back. If you can afford to take damage, this is the best bet you have. Otherwise, Yoshi has a VERY good ouki game at close range -- one that hits you for 40-60 damage if you guess wrong. If he starts to get wise and waits for you to wake up, use wakeup K/A.
If you ARE in close range against him, bait his attack. I find that Yoshi has the most advantage if Ivy tries to out-attack him with counterhits and other shenanigans, but this is far less effective if you keep a solid defense + poke/pushout game. Unless you're extremely confident that you can beat/punish Yoshi, don't even try. If you don't carelessly attack, he'll have a harder time landing iMCF on you and you can react much better against dragonfly.
Long story short, defend using primarily CL, attack from CL -> SW -> pushout to CL. Yoshi cannot catch CL Ivy; abuse it. If you're extremely good with WP zoning, abuse that too.
My two cents.
PS. Shoutouts to Hajime and Ted for kicking my ass with Yoshi. Lol.
