First, welcome to the Forum!
Second, you're overwhelmed because planning a trip is a lot of work, even for those of us with experience. So, break it down into manageable chunks.
The reason you won't find a tour package with your destinations is that they are not typical ones. It's like someone saying, "I want to visit Dallas (to see family in Plano) and then the Gateway Arch in St. Louis - how come I can't find tour packages that include these?" There's nothing wrong with what you want to see, but if these really are your goals, you'll have to do it on your own. Don't worry - we're all here to help!
If these are indeed the places you want to see, and you don't have time to see other places in Italy on this trip, you would fly into Palermo airport to see Palermo and Vicari, and Naples airport for Capri. As said above, you really don't want to base a whole segment of your trip on the Blue Grotto, since it's not always visit-able. However, there are lots of great things to see in the area, including more of Capri, Sorrento, the Amalfi coast, Pompeii, Herculaneum, and Naples.
As said above, Naples and Palermo aren't the easiest places to start with Italy. If you have time, it would be better to ease in with Venice, Florence, and/or Rome first, then work your way south to Naples/Capri and finally Palermo. This also has the advantage of putting Palermo last; by then, having been in Italy longer, you'll get more out of your family visit.
You have time on your side. Since your planned trip is a year away, you can start learning more about travel and about Italy. Do that before you make more specific plans. Get Rick Steves Europe Through The Back Door, to learn the "nuts and bolts" of travel and travel planning, and Rick Steves Italy to learn more about popular destinations in the country. You can get these from the library or buy cheap used copies; for your current purposes, don't worry if you don't have the newest edition.
Also, watch videos. Rick's are here; be sure to click on "Travel Skills" as well as "Italy": https://www.ricksteves.com/watch-read-listen/video/tv-show
How long can you spare for this trip? That will influence everything else. If you have little time, you may want to just stay on Sicily. It takes time to get there, and it's a very large and diverse island. I was there for 11 nights and only hit some highlights. Your trip will be MUCH simpler if you just do Sicily, unless you have a few weeks.
While on Sicily, you may want to rent cars (two if you are a group of six) rather than hiring a driver. If you're communicating on Facebook with relatives, I assume at least some of them speak English; they should be able to meet you in Palermo and help with other logistics.
Where do you and your family members live? That will determine the best airplane routes. Unless you live in New York and can go on certain days, there are no nonstop flights from North America to Naples or Palermo, so you'll have to connect at least once (likely twice).
Again, welcome to the wonderful world of Italian travel. I've been seven times, and would go back tomorrow if I could!