A great trip in Brooklyn this time of year is the Brooklyn Botanic Garden. I try to go every year. It's actually a great trip in the Fall for the leaves, April-May for daffodils, tulips, and Cherry Blossoms and June for roses. It's a an easy trip and kids usually appreciate the beauty of the flowers and quiet of the garden in general. I do highly recommend telling the kids that it is NOT a park, so they need to behave as if they were in a museum.
I always go to see the Japanese Hill and Pond Garden. I love it, the kids love it, especially looking for carp or turtles and exploring the temples, and it takes a good 20 minutes to see the whole thing. I also like the biome pavilions. They have the desert, warm climate, and tropical. I sometimes skip the tropical one so my hair doesn't frizz out like a poodle, yes it's that humid.
They have a Mother's day plant sale every May but I haven't been to that in years, so I don't have any info on prices or times. The rose garden is really pretty and so are the Cherry Blossoms, even when not in bloom. They have several other gardens but I've never taken the kids. The Children's Garden is closed for construction right now.
The garden is off of Eastern Parkway in Brooklyn. You can take the 2 or 3 to Eastern Parkway - Brooklyn Museum stop and it's about a 5 minute walk from there. The B, Q, and S go to Prospect Park station, but that's a bit of a hike - about 15 minutes - to the entrance because of the construction. And the 4 or 5 to Franklin Avenue, I've never taken this stop so I don't know how long the walk is.
There is nowhere for the kids to eat in the gardens, but they can eat on the steps of the Brooklyn Museum and watch their fountains, there's a park with benches right off of eastern Parkway on Washington Ave, and there's a playground on Ocean Avenue, about 15 minutes away. The trip is free is you do a self guided tour but they do have paid excursions as well. I've never done those, so I can't tell you how they are.