12 day trip itinerary help- Istanbul to Athens with Greek island stop

I don't see any direct flights via Istanbul, so I think you will have to accept flying through Athens if you wish to go to an island.
Do you plan to go anywhere else in Turkey aside from Istanbul?

May 5 is Orthodox Easter.
May 6 is Easter Monday.
May 7 is International Worker's Day (May Day).
All are public holidays in Greece, with union stoppages likely on May 7.

Thanks for your response.

We don't know how to best allocate our time between Greece and Turkey, and if going elsewhere in Turkey (or Greece) is a worthwhile use of our time, we would be open to that. I fear spending too much time moving from place to place, but if it is worthwhile, please let us know. We appreciate it!

Thanks for your response regarding the Easter-related holidays.

Since May 5, 6 and 7 are national holidays, how does that affect our activities. Is that a good time to be in Athens, or should we use those days as our Greek island touring days? Or, is travel to/from the Greek islands difficult before, during or after those holiday dates?

Thanks in advance for any additional guidance.

Well that is really up to you! I believe there are some ferries out of Izmir, so that is a possible strategy you could use to avoid transiting through Athens. Once you are on a Greek island you could probably make your way to Athens rather easily with a direct flight or ferry.
Some people just don't think they are going to Greece unless they go to Santorini for example, so we need to know more of what you are thinking about your itinerary. Maybe spend some time with guide books and then come back?
Hopefully someone can spell out the effect Easter will have on travels, as I cannot advise on that and it may be quite significant. I do know you could easily fill your time in either country.
It is way too early for beach or party season if that is something your kids were interested in.

When we went to Santorini, we took a day tour to another nearby island and walked up to a volcano. We booked the tour through our hotel so I don't remember the name of the tour provider.

Normally strike day in Greece is May 1. However since Easter is late this year May 7th has been designated Strike day. Ferry and flight service may be curtailed. Bus service may also be interrupted. That date you probably want to be safe and sound on an island with no intention to travel until the day after the 7th.

With stan's helpful info, I would work backward: First, decide how important Athens is for you and how many days you wish to be there. It could be that you fly in on the 8th, see the Acropolis, have a leisurely day exploring and depart on the 9th. Or, if you were especially keen, you would come in on the 6th and have a few days in order to fit in the museums and such.
Then you will know how many days you have to work with. Istanbul could be up to a week. A bit less if you like a quicker pace. I would want at least three full days (four nights).
For the in-between, you really have endless options, as you are considering two very large mainland areas plus the islands.

If you do keep Santorini in your itinerary, only a stay /-3 days maximum. Spend more time on your second island such as Naxos or Paros.

Normally the Acropolis and the Acropolis Museum are closed on May 1. Since May Day has been moved to May 7, the Acropolis Museum website says it will be closed May 7. I can't confirm this is also true for the Acropolis. The National Archaeological Museum is closed Easter Sunday.

Thanks for all the kind replies.

Based on them, and my wife wanting to see Santorini/Nexos, we will visit Istanbul (and maybe Cappadocia?), Athens, and Santorini/Nexos. We still have concerns about Labor Day on May 7, and Easter celebrations on May 5 and 6. We will avoid travel on May 7 due to potential Strikes/closures, but wonder if it is smarter to spend the May 5-7 period in Athens, or on Santorini/Nexos. If the latter, we would probably need to fly out of Santorini/Nexos on May 8 (my birthday!) to be able to be sure to catch our 10am plane home from Athens on May 9.

What do you nice people think - Athens from Approximately May 1 to May 4, and Santorini/Nexos from approximately May 4 - May 8, or the opposite (due to closures in either place from May 5-7 due to the holidays). Please provide any input on the factors you feel are relevant (closures), crowdedness, transportation difficulties, Etc.

Thanks