The beginner putter has no precision. It also has no balance. That is why your long distance putts are rarely accurate. This is the intended behavior of that club.
The beginner putter is there for people to get a basic feel for how putting works in the game. It is not intended for long term use or competitive play. If you choose to use it then you must acknowledge that no precision and no balance means the putt (especially the long ones) will rarely go straight.
The starter is miles ahead of the beginner, don't waste your time with the beginner.