How to manage a project that's very late due to legal issues with the contractors?

Hopefully it would have been specified as a stipulation in the contract that the company you represent cannot be held responsible for any delays caused by contractors be it legal or otherwise and your project plan also account for it in the initial planning phase. If not, its ok. You have to deal with it now

The First step is to communicate with the said contractors and get an exact or atleast estimated date as to when the legal issues will be resolved. Get this date via email/ official letter.

Create a new subsection in your project plan to account for this delay and get all costs related to the same. At this stage do not try to lower your budget. First get the costs, then look for cheaper solutions. If you try to do both steps together you end up cutting out vital processes for the sake of the budget and when it comes to execution, you end up with the process but not the money for the same.

The second step is to communicate with the client via official email and/or letter about the delay and its cause stating the date as specified in the email from the contractors and proposed solution.