Hello,
I’m not Matt but I read your post.
1. I’m pretty confident the 2 wire distributor will not work on a 3 cylinder vehicle. (If I’m reading this correctly).
2. Are all three spark plug leads not giving spark. Where I’m going with this is if your getting spark on two but not on the other, try ohming out the wire.
3. If no spark on all three,I would look at the cap and rotor. Is the rotor making good contact.
Getting a Chinese cap and rotor might be a tough problem. It has to fit perfectly. I can appreciate that your daughter loves the buggy.
Keep us posted. Curious to what you find.