Lots of choices.
Lafarge Lake in Coquitlam has shore access all around the lake but it's not too big and fishing pressure is generally quite high.
Como Lake, also in Coquitlam but a bit closer to Vancouver, also has shore access all around it but more trees along the shoreline, so that might be an issue. The lake is also a bit smaller than Lafarge but seems to be less fished.
Rice Lake in North Vancouver is a good destination since there is a nice walk through the forest, but the only good open shore access spot is the floating pier. That being said, the pier is new and can handle quite a few kids, IF there are not too many other users (unlikely on weekends).
Mill Lake in Abbotsford has excellent shore access all around it. I like the foot bridge on one end of the lake where plenty of fishing space is available.
Green Timbers Lake in Surrey has shore access but in my opinion it gets too crowded at times so best spots are often taken, not ideal for a group of kids.
Browning Lake near Squamish can be good once they stock it, it seems to be fished very little, but the highway next to it might be a turn-off.