Here is what's working:

import UIKit
import Foundation
import SwiftUI

class QuickCalculationsViewController: UIViewController
{
   let contentView = UIHostingController(rootView: QuickCalculationsView(settings: iDSMenuSettingsModel.shared, tabBarModel: VerticalTabBarModel(), calcsViewModel: SubCalculationsViewModel()))

  // MARK: VIEW OVERRIDES
  override func viewDidLoad()
  {
    super.viewDidLoad()

    addChild(contentView)
    contentView.view.frame = view.bounds

    view.addSubview(contentView.view)
  }

  override func viewWillLayoutSubviews()
  {
    super.viewWillLayoutSubviews()

    contentView.view.frame = view.bounds
  }
}

The problem is that I'm having to have the 'contentView' as a property so that I can access it and change it's frame in the 'viewWillLayoutSubviews' function, but that means I can't pass in references to view models created in the UIHostingController constructor

i.e.

tabBarModel, calcsViewModel (and other ones I've trimmed out) would like to be set at the same time inside both the VerticalTabBarModel and SubCalculationsViewModel so they have a reference to each other (and can pass data to each other)

The only way to do that is to create those models in the root ViewController atomically, and then pass them into each other, and then use the final versions in the UIHostingController constructor.

But then I don't have access to it for the 'viewWillLayoutSubviews' function.

But if I remove the viewWillLayoutSubviews then the UI doesn't work on rotation and it doesn't even layout correct on first display.

Where am I going wrong?