The first thing I'd recommend doing is taking this kind of thinking...
...completely out of the equation.
It's clear here how upset you are about this. It's even more clear that you're blaming that band (and that particular guy) as opposed to simply owning up and saying your band has to do something differently, or better - to start landing more gigs. That attitude I'm sure is seeping out into your entire band and others around you. All you need is one person with a big mouth to start saying, "Heathenheart is blaming so-and-so for their inability to get gigs!" That starts to make your band look bitter, childish, unprofessional, AND if the clubs really like that band (as it seems they do), well... you can forget it. You'll be laughed at and won't get booked despite how talented you might be.
It's MUCH better IMO to think nicely of them, wish them the best always, and then do whatever it is YOU need to do to start securing more gigs. People who get gigs aren't the petty, angry take control and screw everybody else over people. They're the people others like, the friendly happy people who learn how to communicate well and work with people professionally. Please do yourself a favor and work towards changing your attitude and view. I don't see any winning scenario if you hold onto it. That band is there. They're getting gigs. Deal with it and let go of any bad feelings, envy, jealously etc. It might not be easy, but it's doable.
I'll add as others have stated that they can't be playing every night of every weekend. Most clubs I know of won't book a band more than 2X a month. That leaves 8 or more Fridays and Saturdays available for each club that you're talking about. If you're not getting gigs, I can't see it being that band's fault.
Erase them from the equation and figure out how to start getting more gigs.
