Cumbo, it is hard to answer without a little more info on your girlfriend's and your style of travel. But I LOVE traveling and diving Cozumel, so will share this one family's experiences. Ferrying over to Cozumel from PDC daily would be a pain in the __. In fact, one aspect of a dive vacation in Cozumel that I love is the rhythm of the dive day, which would not work with a daily ferry ride. For example, most 6-pack dive ops (the ops like Blue XTSea, Blue Angel, Diving with Martin, etc), will pick you up at your hotel pier at 8 AM. You will do two delicious and sublime dives, ending around noon, at which time they drop you back by your pier. If you are using one of the smaller boutique shops, they will keep and wash your gear... if not, you have to haul your gear somewhere and rinse it, unless you rent everything. (I write this assuming your beginner girlfriend is already dive certified... if not yet, that changes the pace of your holiday diving considerably). If you want to do afternoon dives you can do that too... we usually relax with some brews or margaritas and explore the town of San Miguel, or nap by the pool. We stay at the Park Royal all-inclusive, and overall have had 3 years of good experience and the food there is better than similar priced AI's like Hotel Cozumel (although, if you can deal with boring food at Hotel Cozumel, a lot of people love it for the convenience and layout). I also like Park Royal because it has a piece of its property right on the water (rare closer to town), a tiny little sand beach for a bit of sunbathing (again, rare as a lot of the Cozumel hotel coast is rough sharp rock), and there is good safe access to the water there for casual snorkling (very very rare on that main stretch of Coz hotel coast). If I was taking a break from big-hotel, AI experience in Cozumel, I would try the Blue Angel Resort, which is rumored to have a more intimate experience, decent restaurant, and a decent dive shop on site.
For your whale shark experience... I have done a lot of internet research on how best to do that from Cozumel. My decision for us when we try that is to do it in two stages of vacation. At the very end or beginning of the trip... fly into the area of Holbox or Isla Mujeres, do the whale sharks, and stay in that general area overnight. Then start a fresh new day and get to Cozumel as a totally separate stage. Likely using some type of van transport from where we stay at the whale shark area, and get down to PDC, and ferry over to Coz, take a taxi from the ferry to the hotel (typically about $8 US, so not bad). If you want to do a ruin, Tulum is beautiful and a nice half day trip south of PDC. I do not want to mess with your enthusiasm or travel creativity... but adding in a cenote dive on the mainland, with all the things you want to do, is likely not going to be value-added for this trip. Just my two cents, especially in light of the fact you are new to Cozumel's reef diving, and likely do not realize there are months of new experiences to have just there.
Once you are on the island of Coz, you could fill every morning half day with diving (throw in a night dive), and have a totally different and wonderful and satifying experience. The town is neat, inviting, and pretty to explore, the people very friendly and gracious. We always feel safe there strolling and visiting. A neat day trip on Coz is to rent a car for about $50-75 a day, and drive out to the wild beach side of the island... mosy along bar to bar, or beach to beach, exploring the cool shore caves and geysers here and there (at Rastas/Marleys and up to Coconuts). We LOVE to stop by Rastas/Marleys on that wild beach side, get a beer in the hammocks, and then get a massage right there above the bar with the sound of the surf crashing in outside. Marvelous. Very relaxed gyspsy style day, if that is your thing.
Have a great time designing your perfect trip. Happy travel!