You can dress the kids in some nice clothes, but nothing really fancy, especially if you are not going to the formal nights. You may want to re-think about going to the dinning room for the formal nights, they are really special and usually a good menu to choose from, even then you can dress the old 3yr old in a pair of nice pants and a shirt, will be fine.
In most cases you will be sat with another family with kids, although we cruised with our kids and one time we were at a table with 3 other couples, no kids. They said they didn't mind and thank goodness my 2 did behave and were not a problem, but it would of been nice all around if there were some other kids at the table. Hopefully you will have another family eating with you and the kids can meet the others.