What is "lame" is saying "a non-union airline is coming in violating our contract and undermining our leverage."
There are only two parties to the contract. Those parties are CAL management and, possibly, its successors and the CAL Pilot Group. Neither Skywest pilots nor Skywest management are parties to the contract in question. Neither Skywest pilots nor Skywest management can "violate" a contact to which they are not a party.
Nothing a Skywest pilot or a member of Skywest management can do can undermine or enhance your leverage. Your contract is your leverage and it stands on its own. The terms of your contract provide whatever leverage there is.
You'll have to speak with an arbitrator or a judge to get your contract enforced the way you want. In the meantime, I'll be happy to give you a ride to work. I'd appreciate the same consideration from you and your fellow pilots. Thanks.