Welcome to my Swiss Alps.
I'll start with some comments, and hope to fill in a bit more later. Likely, others will jump in.
<<"April 16th- Open Day and need suggestions to see anything in Zurich or around there. Would prefer to see natural scenic places along with some kid friendly options.">>
Zürich is a great city, full of culture, restaurants, shopping. It is my favorite. It is not in the Alps and not known for its natural beauty or scenery.
There is science museum (Technorama) at Winterthur, and it does try to have attractions for kids. 7 years old might like it; 3 yrs old....possibly not.
Unless you already have specific things that you want to see and do, some place other than Zürich would meet your goals better. If you know Zürich, I would not try to dissuade you from visiting.
<<"April 12th: Interlaken, Jungfrau and Kleine Scheidegg (start early in the day like 7am) (What is the best combination for a scenic route)">>
The best route can be determined from a map and the timetable. (see links below.)
The most scenic and fastest (via Meiringen) takes 4 hours and departs Luzern at xx05 every hour.
Going via Bern is another option, takes about 1/2 hour longer, and is less scenic.
Stay in Luzern to go to the Rigi. Why go to Zürich first?
Check this map:
Zoom in for details.
The timetable will guide you, as well:
Boat service is limited in April, but you might be able to take the boat to Vitznau and the cograil that connects with it to the top of the Rigi - "Rigi Kulm."
Check this link and scroll down to "seasonal timetables."
Perhaps your children would enjoy a visit to the Transport Museum in Luzern after you return from the Rigi? There is also a very nice children's playground by the lake at the Transport Museum.
map.search.ch/.en.html ?pos=668256,211413&z=20 48. It is called the Lido.
A famous vegetarian restaurant in Zürich is Hiltl.
www.myswissalps.com/ab outswitzerland/culture history/food
At high altitudes- such as Jungfraujoch or Kleine Scheidegg, it s pretty much still winter.
Even near Luzern, at lower altitudes, ther may be sometraces of snow on the shaded places on trails. However, you are wise to base at Luzern at that time of year. I hope that you do not have much rain.