My husband and I are both teachers, so we've been that week before and will be going again for Easter Break this year. It really ISN'T that bad, if you plan ahead and outsmart the crowds. Try to get to the parks about 45 minutes before the gate opens (even on Early Entry days.) We always eat breakfast in our resort room, to save time and money. Eat lunch and dinner early too, unless you have made priority seating arrangements. Try to get lunch right at 11:00 because crowds form right after that! Make sure you use Fast Pass, and have a plan in mind when you get to each park. Know what rides your're going to need to do first, and which rides you'll use Fast Pass for. After lunch, if the crowds seem too bad, you can head back to your resort to enjoy the pool and rest up. I think you need to emphasize to your family that being on-site will save you time and sanity, will allow you to use the Early Entry which is important for very crowded times, and will allow you immerse yourself in Disney, which is harder when you are off-site. One great thing about Easter week is the weather. You don't get the horrible heat or so much rain, like in the summer. We even have needed a sweatshirt for the mornings!
Good luck!!