Long response, but I hope it helps
We went last year the week leading up to Easter. We actually left the Saturday right before, long drive home.
Best part about going at that time was the park hours. The parks were open late, Mk was open until midnight! And they ran the parades twice. We caught the last Spectromagic one of the nights we were in MK and it was great, uncrowded.
Take advantage of the fact that you are at the Poly and take mid day breaks. I know you said it is your first trip and you probably want to go, go, go and see everything. But if you feel that you are getting tired or your kids are cranky, take that break. It will do wonders.
Use Fastpass if a line is longer than thirty minutes.
Make Priority Seatings if you haven't already. Restaurants were packed with people being turned away.
Stay flexible and be willing to change your plans.
On Easter, some of the resorts have activities for the kids. Easter Egg hunts, that sort of thing. Ask when you check in. I was really bummed that we missed that, but we had to work around hubby's schedule.
The Easter Bunny makes appearances in MK, right near City Hall in a little courtyard type area. Of course we missed this too. As soon as we got in line it was announced that the EB was leaving to go check on some eggs......oh well, at least we got a glimpse of him.
You can ask at City Hall about appearance times.
Here is how we worked our schedule, kind of. WDW was the most crowded I had ever seen it and we still felt like we saw what we wanted, didn't wait long in any lines, and had a nice relaxing trip with plenty of pool time.
Arrival Day--Saturday around 6pm. Checked in, got to our room, ate dinner in the room. Went to DTD until 11.
Sunday--Slept in. Hung out at pool. Went to Epcot at 3pm. Saw Cranium Command, Rode M:S, rode Spaceship Earth, went to Mexico. Rode El Rio del Tiempo, ate at the Cantina, walked around World Showcase a bit, after dark rode Test Track twice with no wait! Then we left.
Monday--AK Early Entry day, but my crew slept in a bit. Arrived for our 10am PS at Breakfastasuarus. Park was very crowded so we did five attractions then left. Swam in the evening.
Tuesday--MK. We got there around 8:20, which is good for us. I used the Unofficial Guides touring plans and we didn't wait in any line longer than 15 minutes. Got my daughters hair cut at the Barber Shop and watched the 3pm parade from there. Left to nap and eat in our room. Returned around 6:30 refreshed and closed out the park.
Wed--Pirate Cruise for the kids at the GF. Back to resort to nap, swim, play tennis, shop. Dinner at the Poly.
Thurs--Epcot, again a late start to our day. Did everything we wanted to.
Fri--MK, not as crowded as other days. Did everything we wanted to. Left around 10pm
Take jackets or sweatshirts in case. It was very chilly last year at that time.
Good luck, enjoy your trip!