wolfish,
if your son throws his shoes behind the fridge then you’re right that you didn’t do an aveirah, you were an ones. Maybe he was testing you to see of you’d beat up your kid or yell at your wife due to the stress of being delayed by the missing shoe. But if he threw his shoe 3 hours earlier and nobody noticed until 5 minutes before shul then perhaps you’re not an ones because you should have made sure your kids were ready earlier just in case.
btw, I hope it doesn’t sound like I’m talking down to you. I’m talking to myself too. I can’t tell you how many times I’ve been late to mincha on erev shabbos because one of my sons was missing his shoes or coat.