Marian, unless you are cruising during a school break period, you shouldn't be inundated with children on the Mariner. However, I guarantee that most of them will be dining at early seating, so you might want to change to late. Once you get onboard, you can check out the early seating passenger mix in the restaurant and if it looks acceptable, make the change (be sure to tip the Maitre d' to get a great table with no kids around)
Generally, late seating always sells out first, so it is more difficult to do it the other way around.
Have a great cruise!