It has been many decades since I visited those parks, so some of my advice may be dated.
(1) TIME: Time allotment depends on how much you want to do. Also, parks are extremely crowded this year. Everything will take much longer than you expect. I suspect that you will only be able to do 2 parks with your time constraints.

(2) GRAND CANYON: Note that GG has South and North rims. South is well developed with hotels, restaurants, etc. North was extremely isolated, and very, very primitive (basic cabins were about it). Although the rims look close on the map, don't even think about driving between them.

We went to the South Rim at Xmas-time, and froze our butts off. I think that it will still be very cold in April. We also went to the North Rim in June. The day before we arrived, the roads were still closed with 16 FEET of snow.

(3) BRYCE/ZION: We went to Bryce and Zion in the summer, so I can not speculate on the weather in April. The 2 parks are very close. Bryce is my favorite (in my opinion, more spectacular than GC). If possible, take a horseback trail ride in ONE of these parks. I did rides in both parks on the same day, resulting in saddle sores the size of grapefruits. Also, I would advise bringing a cheap P&S camera.

Hope that this helps. Enjoy your trip.