By all means, bring the kids to dinner. If it makes you feel more comfortable, you might want to ensure very soon after you board that you have a table for just the six of you. Either fancy or just dressy will be fine. They will most likely take a photo of you at your table on a formal night--what a wonderful memento that will be!
I'd bring a stroller--a lightweight one, if you have it. First, you need to ensure it can fit in the cabin with you when folded. Also, the little ones might get tired during your time onshore. I wouldn't bring the stroller to the dining room, though, as there's not a lot of room for it. The dining room staff will ensure that your youngest has a high chair and that your 3-year-old has a booster seat, if needed.