I'm a little late getting this in, but here's how I played this challenge.
My strategy started with lot choice. I wanted public trash cans, frog log spawners, and public playground equipment nearby to ensure NPC children walking by regularly. I chose the 40x30 lot in between the pirate ship and monkey bars in Newcrest. I only left the lot once.
I had one child be the designated trader for the family. She held all the cards available for trade and spent most of her time talking to every NPC child in the neighborhood. She loved the outdoors so the associated +2 moodlet helped keep her happy while out trading.
The other three children spent their time training. I didn't know geeks had better luck finding cards so only one of my children was a geek. Personally, I found it annoying because even though he spent hours every day training Voidcritters, he still got tense from not playing video games.
As for school, I had forgotten about the excuse note capabilities with the writing skill. Kudos Minnie Mouse. In my save, each child went four days (focused with homework complete), took four days vacation, and skipped two. That was more than necessary because they all ended with As, but I wanted to be positive not to get any grade penalties and I hadn't play tested the negative effects of skipping school. Oops.
After my trader spent the entirety of the second Wednesday trading without gaining any points for the family, she started training too. I didn't want to run the risk of not maxing the 38 cards we had found. We finished with about 18 sim hours to go. My trader invited her best NPC friends over plus one new kid who happened to walk by to give it one more go. No luck.
It seemed like each NPC child held different rare cards so to get them all you needed to make "good" trades (see Minnie Mouse's description) with as many different NPCs as possible. My trader was really good friends with at least 10 of them (more than any other child sim I've ever played).
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