If I'm understanding this correctly, You might be looking for the 'has' method. I'll try to explain it step by step though since it can look a bit confusing at first. First, you use the with method to eager load your booths. This part is simple.

$clubs = Club::with('booths')->get();

This gets all clubs with the related booths. Now, the problem is that you want to limit the booths you retrieve. To achieve that, you can specify additional query constraints for eager loading queries. To do that, look at the example below. Also, link to docs on that: http://laravel.com/docs/5.1/eloquent-relationships#constraining-eager-loads

$clubs = Club::with(['booths' => function($query) {
	// Additional query contraints
}])->get();

So, what kind of additional constraints do we want to add? Well, you just want to use the has method. The has method only retrieves the entries that "has" at least 1 related model. In other words, you want to retrieve the booths that have at least 1 event so you can do this:

$clubs = Club::with(['booths' => function($query) {
	// Additional query contraints
	$query->has('events');
}])->get();

Link to docs on the has and whereHas methods: http://laravel.com/docs/5.1/eloquent-relationships#querying-relations

That should get what you want.