I think suing to stop production or broadcast would trigger the antislapp law.
Plus there probably is a contract provision with the homeowner allowing the broadcast of the the work done.
However, assuming it would not violate the contract in some way you probably could sue to defective construction , doing work without permits or a license etc
This is NOT legal advice, just a general discussion of the law, as we are not familiar with the specific documents and facts of your case, etc. Please consult with a competent attorney in this area of the law for specific legal advice regarding your particular case, as the advice may vary depending on the facts.
The fact that network or production company were involved in unlicensed contracting is probably not enough to get the filming or broadcasting stopped. They may be right in filing an anti-slapp motion in response to your injunction request.
You may have claims against them for faulty construction or not pulling a permit, and possibly other issues. If you paid them anything, then not having a license could entitle you to disgorgement.
What claims you may have will probably depend on the contracts that were entered into. Take everything to an experienced construction attorney for review.
And you will probably need to hire an attorney to deal with the anit-slapp issues.
An unlicensed contractor is not allowed to recover money for their work which requires a license so you can demand a refund from the unlicensed contractor if you paid him any money, or sue him to get it back if necessary. You may also want to file a complaint with the CSLB. It's a good idea to discuss this with an experienced construction attorney, particularly the anti-slapp issues.
As the other attorneys here have noted, you likely have a case for disgorgment of money paid for construction and/or for damage done to the home. This all depends on the details and your contract. I'm certain that Network A has a clause in their contracts limiting any damages resulting from their breach of a contract to money damages and absolutely excluding injunctive/equitable relief. You'll need an attorney to help you respond to the Anti-SLAPP. If they are successful, they will be awarded attorneys fees for costs in bringing the SLAPP motion to strike.