Gap of Dunloe

There are organized day tours that will visit most of the sites on your list, take you on a scenic trip across the lake, and then arrange a jaunting car ride thru the Gap to Kate Kearney's at the other end. Believe they then bring you back to Killarney via bus or van. Can google "Gap of Dunloe Tours" to see what's on offer.
Alternatively, many people opt to just stop off on their drive around the Ring ... believe that's what you're referring to.
If you're pressed for time an organized tour may indeed be your better option.

For us we took the carriage/boat ride thru the Gap of Dunloe and did the other things you mentioned. That would be a packed day but doable. The Ring of Kerry would need a separate day all to it's self.

I arrived in Killarney around noon and toured Muckross House and the Traditional Farms, drove to the Torc Waterfalls parking area and hiked there (5 minutes), then drove to the parking area and hiked to Denis Cottage and Weir Bridge (about 30 minutes each way) all in an afternoon.
The next day, I parked at Kate Kearney’s Cottage and hiked to the top of the Gap of Dunloe and back. I saved the Ring of Kerry for another day. Trying to do both the ROK and the Gap in one day would be a bit rushed.
All of the sites you mentioned are close together, and you could view them in a day. If you take a tour or jaunting cart ride in the Gap, you can get up and back faster than hiking.

You can drive over the Gap of Dunloe. The people that drive the horse drawn traps don't want you to know that b/c #1. they want you to book a tour thru them and #2. They don't like sharing the road with cars. HOWEVER, this IS a public road and one can drive it. I did this 7 years ago. The key is to drive opposite of the direction of the trap tours. Because if you get behind them, they probably won't let you pass. So go opposite of their travel direction. You'll have to have a good map to see where to access this valley that goes up and over the Gap. Because the turn off and the subsequent roads are not well marked (purposefully I'd say). But if you can read a map and landmarks, you can do it. When you see a trap coming, pull over where you can get out of their way, turn off your car and wait for them to go by. Give them the right of way, smile big and wave! You'll get that time to enjoy the amazing view.

I've driven a rental car through the Gap with no real issues, as Buffy suggests. However I will add a caveat to Buffy's advice. If you go in the "back way" through Black Valley, be aware that the road up to the Gap is very steep and very winding. I learned to drive a stick shift in a town with fairly steep hills, but I really would not have enjoyed coming up that road with a manual transmission in the "wrong" hand. If you really want to go that way, do yourself a favor and rent an automatic. Otherwise, go in the "front way" and politely endure the sneers. BTW, we did the southern half of the ROK and the Gap in one day: Kenmare to Waterville, then just north of there cutting east across the peninsula to the Gap, then back out through Black Valley and returning to Kenmare for the night. We had the AA Atlas of Ireland which clearly showed the track across the peninsula and the way out through BV. Sure the country roads were narrow, but that's Ireland. Have a grand time.

We are in Ireland now and left Killarney 2 days ago. We took the 10:00 AM tour of the Muckross House (I do recommend doing this, especially if you are a Downton Abbey Fan), We then walked to the Torc Waterfall (maybe 20 to 30 minutes). If you walk to the Waterfall be sure and take the hiking trail (it follows the road that the carriages are on) since it is nice and green and you might just see a wee small green folk. Actually there are all sorts of trail to hike around if you are interested. We then had a lunch at the café...would not recommend eating here but we only had a lite bite. I had the salad bar (not worth it) and my husband had a premade sandwich...again not that great but perhaps the main dishes are better. We then drove down to the Abbey (very close) and wandered around there. There are no structured tours but it is a nicely preserved abbey and worth a look. The Yew tree in the center has mystical (or so I was told) powers. There was a small tour group there and they were all touching,hugging, etc. the tree. We then went to visit Ross Castle. You can only get into the castle by taking a tour (check the times, I think they ran every half hour) . We had an excellent guide and enjoyed the tour. By then it was probably close to 5:00 PM. The next day we drove to Kate Kearneys cottage parked the car and hiked the gap of dunloe half way. We did get rained on and it was very windy at the crest but it was worth it! Coming back the weather cleared up. Actually if we had time (and the weather was nice) I would have walked the entire way. You just have to figure out the logistics of getting back to your car. There were lots of carriages on the road and I was surprised at the number of cars on there. Towards the top before you start down the other side there were some tight spots so be careful if you drive. I would hike and enjoy the scenery if you are able!