L.B.
I've done a few cruises. One Caribbean cruise with a balcony and one Alaskan cruise with a balcony. I loved having the balcony to hang out, have coffee etc. I thought I would be able to sun there (Caribbean) but it's shaded most of the time. It was still really nice. For the Alaskan cruise it was even better having a balcony. It was pretty cold outside, but if there were whales/dolphins/whatever we could go out and watch them. Also, when we went to Hubbard Glacier, we didn't have to fight for a spot at the railing to see it. My kids were older and had their own state room (in both cruises) But the railings are pretty high. I don't see how a person could "fall" overboard. You would have to physically climb up on the railing. I think it would be perfectly safe for your kids.
The excursions are expensive, but fun. You can do your own excursions for less money, but you have to spend time finding them, risk being scammed, etc. I kind of liked the convenience of booking through the ship and knowing what we were getting.
BTW - one of the best excursions we have done (on any cruise) is the Segway tour in St. Thomas. If it's available in any of the ports you're visiting, you should do it! Our entire family LOVED doing that! We didn't even care about what we saw along the way...it was just fun riding the Segways! There were kids on our tour, that were about the ages of your kids, who were having a blast. You can probably research that before you leave and book a tour on your own when you arrive - ahead of time can be risky. Our itinerary changed mid-cruise because of weather.
Bon Voyage!!!