Welcome to the group! I added you to the June 15th Cruisers list (see link in my signature line) and also there you can find the link to add yourself to the Roll Call Spreadsheet.
We are doing this cruise and the next one back-to-back. On the next one, we are planning to have just the two of us going on an excursion from Civitavecchia and leave our teens onboard. I think with the ages of your children, check to see what youth activities will be available on the port days to know that they will be open - I think they typically are open for just such situations as yours - I think you do have to (or at least should) let them know you will be leaving the ship while the kids stay onboard. As our kids got older, we would leave them on the ship while we went into town - somewhere close. This will be the first time we'll go off on an excursion too far for us to walk back without them. But we're doing it through
DCL so we have less worries (and really, so the boys will have less worries) about us not making it back before she sails.
DCL offers a lot of "with families" excursions in ports - so they do tailor the pace of the excursions to be a bit more accommodating vs those that are adult departures only.
Regarding this, you don't have to tell them you are leaving (they typically have asked us though), because they will know if you are onboard or not on their computer. We have never left ours for an excursion (though we tried once, in Costa Maya last April, for a kayak trip, but it was too windy so it was cancelled), but we have gone into port to walk around and left them on the ship. Once we didn't say where we were going and initially didn't plan to leave the ship. But after we dropped off the older ones in the club, the little one fell asleep in the stroller, so we decided to drop her in the reef and walk around the town. One of our kids wanted us at some point, and they paged our friends who were authorized to pick up. They said when they looked up our kids on the computer to get the wave phone #, it showed we weren't on board so they called the friends. They also know as soon as you are back on, as we have been there when they were paging parents of young kids who were there all day while parents went on excursions (this was on the 2007 Med), the kids were crying and just totally done being there for the day (it had been 12 hours and they were 3/4yo), they said they knew the parents were back, but they still weren't answering the page.
But yes, the clubs are open all day in port, they open up before any excursions begin so you can leave the kids if you want to.
Those "families" excursions have been the source of my unhappiness with DCL lately. I have been emailing them to try to get some sort or logical explanation, or, preferably, a change, in the ages allowed. The "youth exclusive", "for kids", "for families" almost all have age restrictions of 5yo+. I will have a 3yo. I can do the mirror image excursion (which generally sees the same sights, but is slightly longer and might include more events), but not the ones for kids. Extremely frustrating. After many emails that just kept repeating a form answer, I finally got someone who said he is looking into it with port adventures to hopefully modify the age restrictions to include younger kids.
I think it has to do with DCL / Disney not having been to those areas before. The ones they have listed already are for ports they've been to before and/or have done Adventures by Disney in. That's why they've been able to get those up already. I remember waiting AGES for shore excursions to come out in 2007 and again in 2010 for the Baltic - they have to arrange and negotiate, etc. for the tours. It's getting close, though... I think we can start booking March 2nd so I know there are people who can book before us.