Melissa:
The weather in April is delightfully pleasant at Disney World. You'll find that shorts and short-sleeve shirts are all you need and a light jacket for early mornings and evenings. Be sure to check the weather online, though, before you go. You'll also want to carry a small hand-held umbrella or ponchos no matter what time of year as rain can hit at any time in the afternoons.
When our children were younger, we traveled into the parks with a backpack my husband carried but found that having the kids wear their own fanny packs became more prudent as they got out of diapers. It not only made them feel "big" but was a way to begin teaching them responsibility while lightening my husband's load. In each child's fanny pack we included an i.d. card with our cell phone numbers, their rain poncho, a small 8 oz. water bottle, a slim jim snack (doesn't crumble/crush like crackers or fruit), and a few bandages. The few dollars it took to invest in these small fanny packs was well worth us not having to lug around a backpack with everyone's poncho and water bottle.
Unless you're fearful of one of your children soiling their clothes, a backpack may not be necessary. I've found that as long as I can fit my own poncho, a hand-held umbrella, a small tube of sunscreen and some hand-sanitizer in a carry-all, I'm good to go. Your need for a hand-held fan, extra clothes or large bottles of sunscreen are not as necessary in April as in the summer. But if you find that you simply MUST take in a large backpack with extra snacks, clothing or other items, consider checking it in at the
lockers that are typically located near Guest Services in most of the parks. The small rental fee will be worth the freedom!
Wishing y'all a magical vacation!
Whitney