I haven't cruised with children as young as your's (our's are school-aged), but we did tip the full amount for each of our children. Anyone who has ever looked under the table after children have eaten understand that cleaning up after children is more labor intensive than cleaning up after [most] adults! Not to mention the extra mess they create in the cabin, etc.
Your tips (unless you pre-pay them) will be charged to your Sign & Sail, but you can adjust the amount any time you'd like. Many people take the tips off completely because they prefer to tip the staff individually. If you want to adjust your tips, keep in mind that the purser's desk is open 24-hours, so you don't have to wait until the last day and stand in that long line to do it. Even if you pre-pay, as we did, you can still tip extra to the staff that really helped you and your family out. We tipped extra to our room steward, our waitstaff, and a camp carnival counselor, because they were all so extraordinary.
We are generous folks by nature, and when we figured out that most of the staff work 7-days per week, get paid very little (since the ships are not under United States registry, the cruise lines can bypass U.S. labor laws and pay their employees very little and work them far more than would be legal in the States), and [most] work very hard, usually to send money "back home". We figured if we could spend $5,000 plus on a vacation (and we are not wealthy - husband is a schoolteacher, I am a business manager), we could certainly make sure the staff that helped us were appropriately compensated. This was just "our take" on the situation, of course.
Happy Sailing!
JO