I used to live there with kids and (politics aside) it's a wonderful place for kids.
Easter can be sunny and warm enough for a tshirt or snow. I've seen same in same week. If you are there over actual Easter weekend be aware that a lot closes.
My fave kids activities off the top of my head:
Margaret Island - Margit Sziget. You can hire bikes or a bringo cart to explore. Unfortunately the dancing fountain doesn't start until May and Palatinus strand (outdoor baths - more for kids not same as the famous thermal baths) would be a bit chilly still although there are some indoor parts. Flumes won't be open and are v strict on height. Best play park is on the Buda side at Parkmozi bus stop. The 26 runs from Nyugati station through the island.
Also Margit HÃd - the bridge - best free view in city from middle opposite side to the island entrance.
Funicular railway ride up to the castle. Don't take them in castle though. Walk along to fisherman's bastion instead and go round the turrets - stunning.
The thermal baths are not really intended for children though the main tourist ones allow them. I would only advise this if they are very sensible children who won't be loud and will follow advice not to run and not t our head under water. If planning this take own towels, flip flops and swimming caps (needed for some of the pools at Gellert and Széchenyi)
Climb the stairs to the top of Basilica.
Visit Heroes square and city park (there are trampolines to burn off some steam next to the playground and the agriculture museum looks like a castle) get there on one of the oldest traditional metros - line 1.
On that the public transport is brilliant - get the app Budapest Go. Buy passes for you all (kids that age are not free and not even sure it's easy to get a reduction as non EU or resident- last time I took DD back I just got her an adult pass too as not expensive). The pass is better value and also prevents the risk of forgetting to validate singles and getting fined, they do regular spot checks, especially on tourist popular ones.
Which are... the 2 along Pest side of river and, 17, 19 and 42 on Buda side. Get off at Batthyány Tér for another great vista.
Food - my DC love the sweet stuff - Kürtoskalács Chimney cakes - sold from stalls. Also csiga pastries (means snail - they are basically cinnamon or chocolate swirls) sold in bakeries (top tip the Aldi bakery sections are amazing!) pogácsa are sort of like deep fried cheese scones.heavy but good. And Lángos are amazing - it's a sort of deep fried bread topped with garlic oil, grated cheese and sour cream.
Children's railway in the Buda hills. This is lovely - trains staffed by very competent children. But it is a bit of a trek to get to on public transport.
Olimpic Park by the Danube is a nice location for a playground. There are many more tucked away all over the city
That's the main things off the top of my head. Have a great trip.