When you hired a third-party construction team to work on your project, you trusted that they'd do a good job. Overall, you agree that they are doing that, but they're taking much longer to complete the job than agreed. Instead of the initial 6-week plan, this has turned into a several-months-long process.
At this point, you have asked them when they'll finish, but they have no date in mind. Your business relies on projects getting done on time, and as a designer and engineer yourself, you cannot allow it to go any further. You believe that they're in full breach of their contract and want to litigate.
Can you sue if your third-party construction team isn't working within the confines of their contract?
Yes, but you need to look at your contract to make sure you didn't agree to mediation or arbitration in lieu of a trial or court. As you may know, most construction companies and teams like to have an arbitration clause to work through problems without heading to court. If this is included in your contract with the contractors you brought in, then you will need to go through arbitration.
Your attorney will help represent you during the arbitration session, allowing you to show how much money you're losing on this project being well over its deadline. If the other party can't show any good reason for the delays, you may be able to get out of the contract and hire someone new to take over while holding the original contractors liable for any losses as a result of their breach of contract.