In my line of work I have a use for "masonry", "carpentry", and other
trades. I would like to somehow create a parent company that can
assume all liability while simultaneously providing insurance, and
other benefits to the subdivisions.
So I'm thinking about it as a Parent company, with child companies
owned by the parent company, I'd like to protect my "masons", and
"carpenters" without having them be subcontractors.
Does anyone have any clue whether this can be done legally, or what
type of similar corporate structure should I study?
I don't think that this is really possible. At least not fully and not via a corporate structure.
It is fundamental that entities cannot change their liability to third parties without the consent of the third parties (subject to specific statutory exceptions like the priority afforded secured creditors vis-a-vis unsecured creditors, and the limited liability concept itself).
So, if a "mason" or "carpenter" is negligent, nothing in your corporate structure can relieve that worker from liability. This is true without regard to whether the "mason" or "carpenter" is an employee or an independent contractor, although, in practice, it is less common to sue an employee than to sue an independent contractor. You can pay for construction defect liability insurance and comprehensive general liability (CGL) insurance for them, but they can still be sued and will still have primarily liability.
In general, absent a direct contractual arrangement to the contrary, a "mason" will not have negligence liability for work done by a "carpenter" and vis-a-versa.
Of course, it is often impossible to prevent both from being made parties to a lawsuit for defective work, because the question of whose work caused the problem is often a factual one that isn't clear until an exhaustive investigation by experts has been done. Often both will be sued at the outset and some who are determined to be not at fault or only minimally at fault will be dismissed voluntarily, or with token settlements, as investigations during the course of the litigation reveal who was really at fault.
Now, if you have a contractual relationship with a third party, say the person who is hiring the general contractor, the contract between the person hiring the general contractor and the general contractor can contractually waive the liability of the general contractor and/or the liability of the subcontractor, for ordinary negligence (but not for intentional conduct of a subcontractor since such waivers are contrary to public policy), and can relieve the subcontractors of contractual liability to the person hiring the general contractor.
This is all a consequence of the contract between the general contractor and the person hiring the general contractor, however, and really has nothing to do with the corporate structure of the general contractor vis-a-vis the subcontractor.
You cannot limit the liability of the "mason" or "carpenter" for harm to persons with whom there is no contractual relationship. For example, suppose that the mason negligently nicks a natural gas line causing an explosion that kills a dozen people who just work in the building and destroys the building. The individual mason and the individual mason's firm, will have liability to the people killed which could not have been limited contractually, although it could be insured against. This is true even if the mason's firm is incorporated, although, if the mason's firm is incorporated, only the person who actually did the work and the firm will have liability, not the co-workers of the person who did the work or passive investors in the firm.
However, if the mason intentionally engaged in sabotage directed at the natural gas line, with an intent to harm the person who hired the general contractor or anyone else, any contractual waiver of liability in favor of the mason would be void and the mason's insurance policy would not cover the loss (and would not be allowed to cover the loss as a matter of public policy). On the other hand, if the victims of the sabotage had insurance to cover this kind of event, their insurance policies could cover their losses.
In the other direction, a pre-dispute waiver of a subcontractor's right to file a mechanic's lien against the person hiring the general contractor, is usually not permitted for any reason other than payments of the amounts owed to the subcontractor, as a matter of public policy.