*Quick note: I notice you're a new member and it's worth noting many people on this board like to use acronyms when discussing various Disney rides/sites. I'm providing you the names of rides I discuss in parenthesis just in case you needed some decoding. I've been here a while and still have to stop and think about some of these acronyms as I'm reading others' posts. LOL*
I said above that any park other than Epcot would be a good choice because that's the one park that always brought out the devil in my child. So, here's why I think my daughter (now 7) always had a break down at Epcot until she was about 5. This is from the perspective of a (now) 35 year old father.
First, let's consider size/foot travel because the comments below are directly effected by this aspect. In terms of the amount of area you'll cover on foot, Epcot is the largest of any of the parks. Followed by MK, then AK and finally HS. I did a quick Google search because I was curious and sure enough:
http://knowdw.com/theme-parks/walking-distance-disney-world/
Okay, on with some rationale for why I'd recommend avoiding Epcot with toddlers:
1) Heat/Lack of Shade - At Epcot there's a pretty significant lack of shade throughout. Sure, there are shaded areas here and there. But by and large the shade is quite scarce. There are shops and attraction areas to duck in to but as you're walking around World Showcase (WS) there simply is a lot of sun beating down on you. Obviously the time of year you go will dictate how much that heat bothers you. But, like Philadelphia, it's always sunny in Orlando. You're going to be there in the Spring?... yea... it's going to be hot.
Comparatively: AK has a lot of shade throughout but is also naturally warmer. HS doesn't have the foot travel that Epcot or AK do but has little/no shade.
2) Being stuck in a stroller - I don't think this needs a lot of explaining. Epcot involves a lot of walking as I said above. You pair this with #1 above and you can figure how unhappy a toddler will get after an hour. Even with a cover. We bought a battery operated fan/mister that clipped on to the stroller's shield portion to help keep our daughter cool and I'm sure it helped but I can't gauge just how much because (typically) by our half-way point around WS, the meltdown had ensued. Being wheeled around WS wasn't her cup of tea.
3) Ride Selection to break up travel "around the World" - There simply aren't many places to make pit-stops along your tour of the WS. At least not with the toddler in mind. There's just not much for a toddler to do other than Frozen Ever After (FEA). (And yes, I am aware of all the other ride options such as Spaceship Earth, Turtle Talk, etc but am speaking from our POV; and FEA wasn't open until a couple years ago.) Certainly there are toddler-friendly rides but I view Epcot more as an "adult" park. I'm sure many would agree and I know there are some who would disagree. There are Meet & Greets (M&G) with characters spread throughout WS which may help. But it wasn't enough for us. So when you pair that with #2 above it's a recipe for disaster. But that's my POV. I'm sure others have children that didn't mind it and are perfectly happy to tell us about it.
Comparatively: AK has a "quest" of sorts, called Wilderness Explorers (here's a
link), where they can obtain a map and go on a knowledge-based expedition to get a number of "badges" (stickers, IIRC). My daughter enjoyed that. There's also the Safari and a couple shows and there's the Triceratops Spin (dumbo substitute). HS doesn't have the foot travel that Epcot or AK do but has little/no shade. There's Toy Story Midway Mania (TSMM) that nearly every toddler enjoys (even if they're not good at it). There's Ariel's ride (forgetting the name) and Disney Jr. Playhouse show and obviously various M&Gs. That's really about it for toddlers, though. However, the good thing about HS is that if you were to tour the park you won't find yourself stuck a loooooong walk away from the exit like you might if you were at the apex of WS in Epcot.
I realize everyone is different; especially every child. But that was our experience through the more trying years (2-5 yo). Overall my daughter was a great toddler and rarely ever fussed. But Epcot
always brought out the worst in her. Since she's been about 5+ it's not been an issue. She loves Soarin', Test Track, etc... She loves the character M&G's (as she did before). Generally, Epcot is a fun place for her... now. On our last trip we hopped from MK to Epcot about two hours before Epcot was due to close and we had a blast. So Epcot on our next trip in March will be toured in late afternoon/night.
Ultimately, I'd recommend HS or AK over Epcot for a toddler and the above reasons are why. Hope that helps.