Ann,
Wow...the prices have gone up since we were there 4 years ago!! But, even paying for a private driver, it is still less expensive than taking a guided pre-packaged group tour, and you will get to do exactly what you want, when you want, so it could be money well spent. Would the Kerry Experience tour company provide transport from Shannon thru Doolin and on up to Galway for you, since you are using them for other days? They might give you a nice price to handle your entire journey???
I hope you have an incredible trip. My only words of advice are: If you want to do something, just make it happen....visit those you might want to visit on the trip. Once you make the long journey to Ireland, the extra costs will likely be forgotten later, but the memories will stay with you forever.
I hope your cancer type is curable and that you enjoy a complete recovery!! None of us ever knows what is around the corner in our lives, so we just have to live each day to the fullest.
Safe & happy travels.
Also, you mentioned in one of your posts that you were not sure how much touring you could do on the first day, since this will be your first time traveling to Europe. While there are some people who can just keep going until dark after arriving, we typically start fading around 2 or 3:00, depending on how much sleep we were able to get on the long flights. I think it would be very reasonable to get picked up at the Shannon Airport, then swing by the Cliffs of Moher (allowing about 1.5 to 2 hours to visit there, depending on your energy level), then travel along the coast to Galway, veering off to see a bit of The Burren. In Galway, you would likely enjoy a stroll down Key Street, where there on cafes and street music, then I would suggest a good nap.....or take a nap upon arriving in Galway (after the Cliffs/Burren) and then go back out to Key Street early that evening (and call it an early night). That way you will have good energy for the next day.
And, depending on which cancer treatment you are under, you will want to take extra precautions by using Wet-Wipes, etc. for your plane, hotel, etc. and have a little extra protein while traveling. Also, if you quietly and kindly explain to hotels, airline, etc. that you are battling cancer, it is amazing how kindly rooms can be made available earlier or nicer seats might be quietly made available to you. If you have an implanted chemo port, don't forget to take a letter from the doctor to hand to the TSA agents (will make your screening much easier). Also, if you have long connects to make in places like Newark or NY, go ahead and arrange for the little cart to meet you and take you to your other gate. The Shannon airport is very small, so you won't have problems there. Pack light, so your luggage is easy.
Safe travels and lots of happy memories!