If I was you I would encourage the members of the league to play the tourney and find a way to incorporate the tourny results into your league.
I ensure you that it's NOT a HUGE problem. I used to run Thursday Night Leagues (that averaged 15-35 people) and Saturday morning "Breakfast Club" leagues for YEARS. A few times I worked the Saturday league into a tourny that got planned over top of my leagues.
When you blanket a day and say "every x-day we're having an event" it's going to eventually be over-written. Communication is key.