The huge bash of Queen's Day will be crowding Amsterdam during some of those dates. You should read up on the festivities and see if the performing arts activities will make you want to hang around, or if you want to be well clear of the scene. It's a massive event and might even be more massive this year since it is the last "Queen's Day" because the queen is steeping aside in favor of her son, and it will become "King's Day."

http://www.amsterdam.info/queensday/

Needless to say, if you haven't booked a hotel, do it now!

April 23-28 in Amsterdam cannot be changed. It's part of a business trip.
Right now I am leaning towards Copenhagen or Munich for the first three days of the trip.

Queens Day is still April 30th this year. So that won't affect your trip. What may affect it is the change from Queen to King that day. You can expect certain restrictions in the city, and places like the Nieuwe Kerk and Palace on the Dam to be shut, but I expect the impact will be minimal.
Why not spend a couple of days in another part of the Netherlands first? One of the islands, or down in Maastricht, up in Groningen or Friesland maybe?

Forgot to mention, we will have to travel by public transport only for the trip; not sure if that changes your recommendations...I was also interested going to Cologne to see the Rhine valley, but seems it's a bit tough to travel around there without a car.

I have done a "side trip" to the Rhine Valley from Amsterdam - took the train to Cologne and onwards to Boppard, I think. Once there I took the riverboats for a daytrip - it was very pleasant and easily done. Not sure about the riverboat schedule in April - I was there in the summer. I stayed 3 nights and it was lovely so I would say it is very doable from Amsterdam (or pre-Amsterdam).

Brugge would also work altho in some ways I found it a mini-Amsterdam. And I think you should be safe from the Queen's day party in A'dam. We visited around the time you are going one year and left town on the 28th I think, and everything went smoothly. You are planning to go to Kuekenhoff? for the tulips. Also you can rent bikes and ride thru the tulip fields. Enjoy!

public transport will be very easy and comfortable for this sort of trip

On public transport only you could still get the train to Maastricht or visit Texel island easily enough.
Or maybe if it appeals you could go to Hoge Veluwe NP for the Kroller Muller museum and stay in Otterlo a couple of nights, to make it a more relaxing visit.

Thank you for the all suggestions. Glad to know it won't be too chaotic in Amsterdam from Queen's Day party when we'll be there.
We decided on Munich to go with our Amsterdam trip. It turns out that the plane ticket price would almost double for my sister ($1800 vs. $980), if she flies into Copenhagen instead of Munich (she's not flying from NJ).
I'll save the Rhine Valley trip for later; the river cruise has been on my bucket list ever since I saw the promo video.
Yes, absolutely we are planning to going to Kuekenhoff!