Notes:
the best way to do this exact itinerary is to fly from your home country to Manila, then catch a flight to Coron and then start your journey as described in the itinerary. Flight days/times from your home country and in between the domestic flights are not counted as days in this itinerary (Manila to Coron not counted as a full day). Therefore, plan your arrival and departure dates accordingly.
To get from Coron to El Nido, you do not have to book a 3 day 2 night cruise but you can opt for ferry (book with local travel agency) or fly from Coron to El Nido (expensive)
The 3D2N tour from Coron to El Nido should be booked ahead, we recommend Keelooma. They had awesome spots to visit and the organization was spot on. https://www.keelooma.com/
To get from El Nido to Port Barton, we used a company called Philippines a la carte and booked a shared van transfer with them one day before our departure date (location: https://maps.app.goo.gl/cwoV1dHQKxTvAWFXA )
Cost = 600PHP
To get from Port Barton to Puerto Princesa, we also booked a shared van which we booked online with 12go Asia.
We booked the Princesa underground river tour via klook, this is the exact tour: https://www.klook.com/activity/4087-puerto-princesa-underground-river-day-tour-palawan/