Sicily and Greece?

Not insane, but it depends on how long the trip is. If you really want to get a good feel for Sicily you need at least a couple weeks. Then it depends on what you mean by Greece and the islands because it is fairly large and long. Since your time is pretty much unlimited, then what you want to do isn’t insane at all.

How long were thinking of traveling to them? Our first trip to Greece was for a month, while Sicily was two and a half weeks.

I’m thinking about a total of eight weeks. I hate being rushed and want to have a real feel for a place.

With 8 weeks you should be able to do both at a relaxed pace

It's certainly not insane. Most folks seem to give mainland Greece and the Peloponnese short shrift, so I'd first ask how much time you're willing to spend.

Greece + Sicily could be done on a retiree's schedule, but there's no particular logistical advantage to combining those destinations since there are no rapid ground-transportation links and most likely no non-stop flights. There are some similarities in the experiences (major Greek ruins, coastal towns, etc.), so this would not be a combination I'd particularly favor. I'd shoot for more variety, perhaps combining Greece with Turkey or Bulgaria, or even with a more-distant European country reached by flying. The variety thing is a matter of personal preference, I guess, but I think as you graduate to longer trips it is more likely to be important.

My first visit to Greece was as part of a three week cruise to the archaeological sites of Greece and Sicily. We spent three days in Greece visiting the sites in Athens, including the Acropolis Museum, and then sailed to visit Mycenae and Epidarius. We then sailed for Sicily making landfall near Taromina to visit the Greek Theatre there and then made our way slowly around to Cefalu then up the Italian coast to Paestrum (my personal favourite) and Naples for a bit of Roman archaeology at Pompeii and Herculaneum. I felt that beginning such a trip in Athens provided good context for the Greek expansion into Italy .

With a fairly long trip, this is perfectly logical.

There's a lot of shared history (you will see Greek temples in Sicily that are just as impressive as ones in Greece, the Venetians were everywhere...) so the trip will feel cohesive. Combining wildly different places can be done, but it might be jarring to go from Sicily to...I don't know, Finland or somewhere with little similarity. Some people might care about this type of cohesion, and if so, these two places fit easily together.

As far as logistics, you'd want to fly into Sicily, then fly from Catania or Palermo to Athens, then explore Greece, flying or taking ferries between islands, then fly home from Athens. Or vice versa if you start in Greece. The point is there should be easy flights between Sicily's major cities and Athens, and doing one then flying to the other is the way to go. There might be direct flights from Sicily to Greek Islands like Santorini, but it's more likely you will go through Athens.

I checked skyscanner.com's flight information through August 2022 and found non-stop service only from Catania to Athens; there was nothing from Palermo. From November through March there were flights only on Monday and Friday. Then gradually some other flights were added, but I saw nothing on Wednesdays and Saturdays even in the middle of the summer.

Why insane? I'm doing it in the spring. With the amount of time you have, no problem.

Adding that if you can’t get direct flights, a connection through Rome is an easy option. Rome will have frequent flights from/to both Sicily and Athens, as well as some to other parts of Greece. On an 8 week trip, one day with two flights should not be an issue.

I happened to fly direct Naples - Athens a couple years back, so Naples is another option but I don’t know the frequency of this flight.
On my trip to Sicily I connected through Rome. Into Catania, home from Palermo, both times with a stop in Rome then direct to North America. People sometimes make getting to Sicily sound like some sort of difficult odyssey, which was not my experience at all.