is an appeal for a hug.
Guessing you're a guy, here's my advice, and it might not be perfect.
I am determined to teach my kids honesty and integrity. They know it's important. Getting caught in a lie always gets a much harsher punishment than the alternative of just owning your mistake. Here's an example:
If you play video games before doing homework, chores, and 30 mins of outside play, punishment is no video games for the next day.
If you do this and lie about it. You get 3 spanks...and no video games for the next day.
They will get away with much more than you fear, and you will catch them much more than they want.
As soon as they conspire against you, there's little you can do, except either pray, or play dirty and pit them against each other. Sorry.