Sounds like an intake leak somewhere. It's important to put an o-ring in the carb sleeve where it meets the intake tube or wrap the intake with Teflon tape and tighten the carb clamp good. Make sure the throttle slide in the carb has some light oil on it and it's not binding on the idle screw.
I agree with @Ralphop, it sounds like an air leak, too lean on the idle jet or idle rpm screw turned in too much. After making sure that adjusting the idle doesn't fix it, check all connection points from where the carb attaches to the intake till it enters the jug by spraying it with water (or brake cleaner) at each connection. Water will bog it, brake cleaner would make it race more. If you find nothing there, it might be a leak at a bearing seal.
Good luck with this project! You should feel lucky, not many dads do projects with their sons anymore.
If it's not an air leak it could be few other things:
1. Slide installed backwards or binding somewere
2. idle screw screwed in too far
3. throttle cable too tight (you should have a little bit of freeplay when you twist the throttle)