We started taking our kids on boats when my daughter was three and my son five. I have always been amazed how agile they are on boats. We purchased lifeline netting but never felt the need to put it up. Just basic common sense rules have worked just fine for our kids. Also, my kids know that I modify the rules as the situation demands.
Having a life jacket that is comfortable for the child is a must. Soaking them (the lift jackets) in fabric softener can help a lot! Wear them before going to the BVI so you know if they will chafe, etc.
I don't wear a life jacket all of the time, but I put it on as soon as it gets rough, or the wind picks up above a moderate blow. If someone else falls overboard I know I can stop the boat, drop or luff sails, and maneuver the boat as needed. However if I fall overboard I figure I might be in the drink for a fairly long time with my crew at the wheel. Also, kids are much less likely to complain about their life jacket if you are wearing yours.
I do think it's rather easy for kids to get dehydrated while out sailing. We now keep careful track of their fluid intake (tell them how many bottles full they need to drink each day and help track it). They tend to drink more if you can find an insulated water bottle.
Some kids are rather prone to sea sickness. Our doctor recommended Bonine over Dramamine for kids. It does not cause as much drowsiness. If there is any chance someone will be sea sick, including adults, have them start out the week taking at least a low dose and Bonine. They can back off when they get their sea legs.
I've always really enjoyed sailing with my kids and I'm impressed how well they adapt to boats.