There are as many opinions about this topic as there are people who cruise

It is possible to be switched to early seating. There is a location to request dining changes. Check your navigator when you check in to see when and where it is. The earlier you go there to request the change, the more likely you are to receive the change. The more flexible you are (i.e. willing to take any rotation, instead of saying I want early seating with the APLAPLA rotation, at a table for 4) the more likely you are to be accomodated. Pick the one thing that's most important to you and ask for that.
Since you are interested in early seating, you probably already know the pros for it. I'll give you some pros for late seating, just to keep in mind.
1) You will see the earlier show, when your kids are more awake, and able to appreciate the show.
2) While the early diners are getting ready for dinner, you can still be enjoying the pools, at the time they are least crowded. A second part of this is on port days, you don't have to rush back to the ship to get ready for dinner, giving you more time ashore.
3) Depending on your "home" timezone, late seating may be more in line with your normal eating time at home (i.e. if you're from the west coast, early seating would be at 3:00 according to your body clock)
4) If the kids really can't wait that long for dinner, you can get food from numerous placed including room service, plutos, pinnochios, etc. They can also eat their evening meal with the club/lab, which typically eat a bit earlier than the late seating (I remember them eating dinner at about 6:30 - 7:00 most nights up at Topsiders/Beach Blanket Buffet).
Good luck with your decision.