If you follow the guide lines for tipping, its $10.00 per day, per person. They will provide envelopes the last full day to pass out that evening..
As for extra spending money, that all depends on your shopping/gambling habits, etc. Most of the major islands do accept credit cards and of course US currenty is widly accepted. A good guide line for that is $100 per day. Its always a good idea too, when leaving to have around 20 single dollar bills, they come in very handy for the tips along the way.
As for dress for the semi casual evenings, husband is supposed to have a sports jacket and I'm sure your son will be fine in a nice shirt and pants. There have been times, we've just left the sports jacket at home, many just dress as a casual evening anyway, so thats up to you.
No, no jeans for dinner in the dining room, even for casual night. A pair of docker type pants and a polo shirt is fine, besides jeans are very warm if you are in the Caribbean, save those for the travel days.
You can purchase some bonnine in your local drug store to take, just in case. If your cabin is mid-ship, you should feel less moving.
When you get onboard, be sure to check out the kids activities, they may have some things going on during the evening and you wouldn't need a babysitter, but you can check into that once onboard.