Disney is doing the special promo tickets this year, both for SoCal residents and non-residents. Both promo tickets are good until May 23rd. That week and the weekend before should be very busy.
For April, Easter is late this year. Normally, peak Spring Break is the two weeks before and two weeks after Easter, with the heaviest crowds coming the week right before and right after. But with the holiday so late, that might spread out the school breaks. Some schools are taking breaks in March, others around Easter itself. So I don't know if Spring Break this year will see concentrated crowds during a short period.
May starts Grad Nites. Dates can be found by doing a search on this forum. Some posters don't care, others avoid GN at all costs.
Since DLR is busy all the time now (just varies from standard busy to moderate busy to crazy busy) and low crowd days are not consistently predictable, choose which dates work best for you and your family. (After all, even the lowest crowd day is of no use to you if it is the worst conflict with your work and school schedules, right?) Then come back here to double check that nothing earth shattering is going to be happening in the parks at the same time. The plan your trip! With good planning and organization, good FP/MP skills, and a positive attitude, even a trip during a busy time can be great!