How to get all children blocks in controller Magento 2?

Make sure your controller is same which loads the layout in which your block and its child blocks exits.

use Magento\Backend\App\Action\Context;
use Magento\Framework\View\Result\PageFactory;

class Edit extends \Magento\Backend\App\Action
{
  protected $resultPageFactory;

  public function __construct(
       Context $context,
       PageFactory $resultPageFactory
  ){
       $this->resultPageFactory = $resultPageFactory;
       parent::__construct($context);
  }

  $resultPage = $this->resultPageFactory->create();

  $blockInstance = $resultPage->getLayout()->getBlock('your.block.name');

  $childBlocks = $blockInstance->getChildNames();

  foreach($childBlocks as $blockName){
    $block = $resultPage->getLayout()->getBlock($blockName);
  }

}