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Here's a possible itinerary for a family of 4 with a rented car for a month. Things to do are in Italics.
A few days in Panama City - to see the Canal and other city sights and shopping...
Drive to Santiago for one night to break up the drive with the kids (about 3 hours drive).
Drive to Cerro Punta in Chiriqui - stayed in a jungle lodge for 2 nights. (about 4 hours drive). Bird and animal watching, hiking.
Drive to Boquete for 4 nights. (2 hours drive). Hiking, mountain biking, zip line, horseback riding, coffee plantations, whitewater rafting.
Drive to Almirante and parked the car and take a water taxi to Bocas - staying in remote lodge for 4 nights then Bocas Town for 1 night. (4 to 5 hours drive plus 1/2 hour for water taxi). Snorkeling, hiking, beach, explore by boat - dolphins, scuba diving, surfing.
Back to Almirante and drive to Santiago for one night (again to break up the drive). (about 4 hours drive)
Drive to Santa Catalina (a bit less than 2 hours drive) and stay there in a bungalow for 4 nights. Surfing, snorkeling and jump off spot for exploring Coiba Island (great scuba diving).
Drive to Pacific beach area - options here include All-Inclusive resort, bungalows or golf resort. 4 nights. (3 to 4 hours drive). Beach, ATV tours, El Valle is nearby, horseback riding.
Back to PC for the last couple of days. Embera Village Tour, Barro Colorado, Portobelo are all day trip options if time permits and of course, last minute shopping. Nightclubs and restaurants.
So that's a month in a nutshell - you would see a good cross section of the country without rushing - experience both beach and jungle plus some culture and fun activities for the kids.
You could certainly reduce or expand this itinerary depending on your time frame and interests.