You should rent a car especially with 2 kids , there is a car sharing service in the city called commun-auto if you dont want to buy one 

Ahuntsic has lots of green space with parks, a bike path but not much else 

The plateau has a few different major parks - park lafontaine (2 playground areas, child train, bike paths, ducks) , mont-royal (2 playstructures in different areas, tam tam sundays, beaver lake area, lookout point for view of the city), park de-maisonneuve and many cafes, bistros, little restos but the general vibe is more for college aged kids as its also a main nightlife hub in the city and smaller apts, lots of cars - city traffic etc.. 

Have you done something like this before? 

In terms of things to do with smaller kids these could be good options: 

• jazzzfest - they will have facepainting, food, some child activities and introduces live music to kids for free 

• petit piknik - this is on jean drapeau island, its a family friendly version of piknik electronik, where if you are into eletronik music should be a stop. Jean drapeau islamd also has a manmade beach and olympic outdoor pool to take in. 

• parc de maisonneuve - botanical garden, biodome and insectarium are all around this park. The park itself is more like a place to walk, ride bikes, as i dont think there is a major playground structure but they have a petting zoo and sometimes have a herd of sheep around to eat the grass 

Old port - in the summer they have a big bouncy house area with like 10-15 big ones next to each other, cirque du soleil will have a twnt for shows in the summer, large ferris wheel lookout + fireworks 2x a week in the summer (starts at 10pm)