I would not worry about the kid with the balcony as they do lock and it is such a small area in the room it would be very hard to not notice one of your kids going outside...also the railings are pretty high for kids so unless they climbed on a chair or table they would be no where near falling over.
As for entertainment, your 3 year old could participate in the Camp Carnival, your one year old could not however and you would be on your own with that one 24/7. Some of our friends cruise with another family or they bring another person with them to babysit...for instance my oldest daughter comes on the cruises with a group of us so the couples with the younger children have a few nights to themselves. We are going on the Dream on 11/23...she will be with us if you need a sitter
I guess it really depends on the experience you are looking for. If you want a family vacation where you spend all of your time withthe family then I think you would be fine to bring them, you just don't get a lot of privacy...that is where I would also recommend the blacony...once you put the little ones to bed you could atleast have that area where it is just the two of you. It is good for more than stargazing