You're most likely going to run into a number of school districts' spring break between April 1 and April 20. It's impossible to know because, unlike DLR, WDW has a much larger contingency of folks who travel across the country relative to the local crowd. My children go to public school (we're out east; not in Florida) and their spring break does still coincide with Easter. But, we know others who have spring break in early April. WDW is going to be crowded, but that's okay, just accept it and don't dwell.
During early April, I doubt there will be any shows that only run on certain days. That practice - to the extent it happens, which is rare at WDW - is generally relegated to the lowest capacity times of the year.
MK is the only park that somewhat fluctuates based on the day of the week, and even that trend is weakening (again, due to the fact that a majority of the people there have traveled, taken off work/school, etc.). I would venture a guess that I've been in MK for over 50 days in the past 10 years and I can't recall a single time when I said "oh, it must be a ___day." Day-to-day crowd fluctuations, to the extent they exist anymore, just aren't that extreme to be noticeable. Holidays and extreme weather events, however, can cause them to fluctuate pretty wildly and noticeably. You shouldn't experience either in early April.
Definitely skip the DLR duplicates that aren't on your must-do, every time list - we actually plan to do the same when we are at DLR next year (I think you've responded to some of my questions about DLR haha!). Definitely don't worry about a hopper either - we've done them so many times and each time I ask myself "was that really worth it, or did we just spend all that time to hop because we needed to justify the cost?" The only time a hopper really makes sense, IMO, is 1) if you plan to knock out a ton of table service options while you're there, 2) there's a park that has just like one must-do attraction and you're going to spend maybe an hour there and then not go back, or 3) you are walking distance from a park (like Contemporary or Beach Club) and plan to go into the park every night for dinner or fireworks, regardless of where you spent the rest of the day.
As far as order goes, I don't know that there's a good strategy. It's based on your preference. MK is going to be physically and mentally draining, and will certainly be a 1+ day affair, just like
Disneyland. HS is going to be a lot of waiting in line. EPCOT is going to be peaceful and enjoyable, even if it's a busier day. And it doens't seem like there's going to be a ton left at AK by April due to some major planned construction (it's still a really cool park because of the animals, and Pandora is a sight to see, but there's just not a ton of rides or shows). So, plan those out however works best for you and don't fret about whether you did it in the right order.
Have so much fun! Where are you staying?