I'll speak my mind....
Sounds to me like the DAD should go back and forth to the mailbox and back on HIS bike and stop pushing and pressuring a toddler so that things that could be pleasant wind up being something the kid wants to avoid.

I have a brother like that- always there with his sons- little league coach, cub scout den leader, go cart building, YMCA swim lessons, skate boarding clubs, science museum camp-outs,....poor boys couldn't breathe, and could never live up to everything he wanted them to do well that he never was able to do as a kid. He wanted to relive being a boy with them, but with them cooperating so that everything would be perfect this time around. Not good!

I would suggest to let the kid sit on his own bike and make it move if he WANTS to. Just have someone sit nearby ready to be helpful if the kid asks for help or falls over or walks away to do something else. If someone wants to pull the kid along, I would suggest putting him in a little wagon.

Sorry to open my BIG MOUTH- but I do it so well!