My YFM80-Moto4 will not start with the battery until it is warmed up. To get it started initially, I have to push it. If I dont push start it, the kids run the battery down trying to start it. The carburetor is fine as far as I can tell. Any Ideas???

 

You could try a new plug.. You also might want to check the valves .. (believe me they do make a diffrence in cold starting).
Take the carb off and remove the float bowl and look for dirt/rust, spray a little carb cleaner in it and re-install.
If that doesn't work take it to a mechanic or dealer and have them look at it.